latest research papers on graph theory

Research Trends in Graph Theory and Applications

• © 2021
• Daniela Ferrero   ORCID: https://orcid.org/0000-0003-4675-1814 0 ,
• Leslie Hogben   ORCID: https://orcid.org/0000-0003-1673-3789 1 ,
• Sandra R. Kingan   ORCID: https://orcid.org/0000-0002-8232-5540 2 ,
• Gretchen L. Matthews   ORCID: https://orcid.org/0000-0002-8977-8171 3

Department of Mathematics, Texas State University, San Marcos, USA

You can also search for this editor in PubMed   Google Scholar

Department of Mathematics, Iowa State University, Ames, USA

Department of mathematics, brooklyn college and the graduate center, city university of new york, new york, usa, department of mathematics, virginia polytechnic institute and state university, blacksburg, usa.

• Features research in a broad variety of problems in different areas of graph theory
• Each chapter offers an introduction to a graph theory topic of current research, aiming at clarity and high-quality exposition while emphasizing recent advances and open problems
• Presents concepts and ideas thoroughly and with details
• Each chapter corresponds to research proposed and led by prominent research experts in each field

Part of the book series: Association for Women in Mathematics Series (AWMS, volume 25)

2983 Accesses

4 Citations

2 Altmetric

This is a preview of subscription content, log in via an institution to check access.

Access this book

Subscribe and save.

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime
• Available as EPUB and PDF
• Read on any device
• Instant download
• Own it forever
• Compact, lightweight edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info
• Durable hardcover edition

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

About this book

Similar content being viewed by others.

Graph Theory – A Survey on the Occasion of the Abel Prize for László Lovász

Introduction

The ubiquity of large graphs and surprising challenges of graph processing: extended survey

• graph symmetries
• metric dimension
• graph searching
• data storage
• power domination

Table of contents (6 chapters)

Front matter, finding long cycles in balanced tripartite graphs: a first step.

• Gabriela Araujo-Pardo, Zhanar Berikkyzy, Jill Faudree, Kirsten Hogenson, Rachel Kirsch, Linda Lesniak et al.

Product Thottling

• Sarah E. Anderson, Karen L. Collins, Daniela Ferrero, Leslie Hogben, Carolyn Mayer, Ann N. Trenk et al.

Analysis of Termatiko Sets in Measurement Matrices

• Katherine F. Benson, Jessalyn Bolkema, Kathryn Haymaker, Christine Kelley, Sandra R. Kingan, Gretchen L. Matthews et al.

The Threshold Dimension and Threshold Strong Dimension of a Graph: A Survey

• Nadia Benakli, Novi H. Bong, Shonda Dueck (Gosselin), Beth Novick, Ortrud R. Oellermann

Symmetry Parameters for Mycielskian Graphs

• Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, K. E. Perry, Puck Rombach

Reconfiguration Graphs for Dominating Sets

• Kira Adaricheva, Chassidy Bozeman, Nancy E. Clarke, Ruth Haas, Margaret-Ellen Messinger, Karen Seyffarth et al.

Editors and Affiliations

Daniela Ferrero

Leslie Hogben

Sandra R. Kingan

Gretchen L. Matthews

About the editors

Bibliographic information.

Book Title : Research Trends in Graph Theory and Applications

Editors : Daniela Ferrero, Leslie Hogben, Sandra R. Kingan, Gretchen L. Matthews

Series Title : Association for Women in Mathematics Series

DOI : https://doi.org/10.1007/978-3-030-77983-2

Publisher : Springer Cham

eBook Packages : Mathematics and Statistics , Mathematics and Statistics (R0)

Copyright Information : The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Hardcover ISBN : 978-3-030-77982-5 Published: 07 September 2021

Softcover ISBN : 978-3-030-77985-6 Published: 08 September 2022

eBook ISBN : 978-3-030-77983-2 Published: 06 September 2021

Series ISSN : 2364-5733

Series E-ISSN : 2364-5741

Edition Number : 1

Number of Pages : XVIII, 135

Number of Illustrations : 47 b/w illustrations

Topics : Graph Theory , Computer Communication Networks

• Publish with us

Policies and ethics

• Find a journal
• Track your research

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Open access
• Published: 13 September 2023

Mathematical modeling and topological graph description of dominating David derived networks based on edge partitions

• Shahid Zaman 1 ,
• Wakeel Ahmed 1 ,
• Atash Sakeena 1 ,
• Kavi Bahri Rasool 2 &
• Mamo Abebe Ashebo 3  

Scientific Reports volume  13 , Article number:  15159 ( 2023 ) Cite this article

4896 Accesses

9 Citations

3 Altmetric

Metrics details

• Applied mathematics
• Computational science
• Mathematics and computing

Chemical graph theory is a well-established discipline within chemistry that employs discrete mathematics to represent the physical and biological characteristics of chemical substances. In the realm of chemical compounds, graph theory-based topological indices are commonly employed to depict their geometric structure. The main aim of this paper is to investigate the degree-based topological indices of dominating David derived networks (DDDN) and assess their effectiveness. DDDNs are widely used in analyzing the structural and functional characteristics of complex networks in various fields such as biology, social sciences, and computer science. We considered the F N * , \({M}_{2}^{*}\) , and \({HM}_{N}\) topological indices for DDDNs. Our computations' findings provide a clear understanding of the topology of networks that have received limited study. These computed indices exhibit a high level of accuracy when applied to the investigation of QSPRs and QSARs, as they demonstrate the strongest correlation with the acentric factor and entropy.

Similar content being viewed by others

Network topology mapping of chemical compounds space

An effective technique for developing the graphical polynomials of certain molecular graphs

An exact algorithm to find a maximum weight clique in a weighted undirected graph

Introduction.

In the field of graph theory, specifically in chemical graph theory, a chemical molecule is represented by a molecular graph, which is a simple graph. In this representation, vertices denote the atoms and edges represent bonds or connections. The edges goes beyond simple connectivity; it encompasses the type of bond as well. For instance, a single edge might denote a single covalent bond, while a double edge could represent a double bond involving the sharing of two pairs of electrons.

The emerging field of cheminformatics, which explores the relationship between quantitative structure–activity and structure–property, is gaining momentum as it aids in the prediction of biological activities. Topological indices are important invariants derived from graph theory that enable the characterization of a graph's topology. A topological index is a numerical value that provides information about the structure of a graph. Topological indices help in identifying various characteristics of a graph. Furthermore, the topology of a graph remains invariant under the automorphisms of graphs. Comperisons of the degree based toplogical indices hold a particularly significant place in research 1 , 2 .

The first toplogical index introduced by Wiener, during the research of paraffin melting point. Initially termed “path number”, it was later renamed and has since become known as the Wiener index. Researchers have put a lot of effort into studying chemical graph theory. A key component of graph theory's work involves honeycomb networks. The honeycomb shape, with its hexagonal pattern of cells, finds a wide range of applications across various fields due to its unique structural and geometric properties. Some of the notable applications of the honeycomb shape include as: In structural engineering and architecture the honeycomb structure's hexagonal arrangement provides exceptional strength and stability while using minimal material. This makes it suitable for applications in construction, such as in lightweight yet strong support structures, building facades, and panels. On the other hands, in art and design, the visually appealing hexagonal pattern of the honeycomb has inspired artists, designers, and architects to incorporate it into their creations. From decorative elements in interior design to art installations, the honeycomb pattern adds a unique aesthetic.

In this article the notation E denotes an edge set and V denotes the vertex set of a graph G. The expression \(\eta_{G} \left( v \right)\) is the number of edges overall connected to a particular vertex v.

For the sake of simplicity, assume that a and b are two adjacent vertices and E is an edge between them, then the edge partition of E is denoted by \({E}_{a,b}\) and formulated as \(E_{a,b} = \{ \eta_{G} (a)\,,\,\,\eta_{G} (b)\}\) .

The degree-based topological indices shows a significant role in the field of mathematical chemistry 3 , 4 , 5 , 6 , 7 , and widely used to develop models that accurately predict the boiling points of alkanes with carbon atom 8 . Some current discovered degree-based neighborhood indices are presented in 9 , 10 and shown strong connections between entropy and the acentric factor.

In 11 , 12 , 13 , 14 , 15 , 16 , different chemical significant graphs' topological indices are considered. Baig et al. 17 considered the topological indices for several silicates and oxide networks. Ullah et al. 18 , compared and examined the computational characteristics of two carbon nanosheets using some innovative topological indices. The topological characteristics of rhombus-type silicate and oxide networks were explored by Javaid et al. 19 . Recently, Koam et al. 20 , established the entropy measures of Y-junction based nanostructures. Ali et al. 21 give some properties of ve-degree based topological indices for hex-derived networks. In this study, an examination was conducted on distance-based topological polynomials that are associated with zero-divisor graphs, as discussed in 22 . The authors of 23 obtained the polynomials of degree-based indices of metal–organic networks. Zaman et al., determined the kemeny’s constant and spanning trees of hexagonal ring network 24 . Some upper bound and lower bound of graphs and also the spectral analysis of graphs are discussed in 25 , 26 , 27 , 28 . In this research, inspired by earlier studies, we establish some exact expressions of the different types of Dominating David derived networks and their comparisons.

We have calculated the forgotten index ( \(F_{N}^{ * }\) ) 29 , the second zargeb index ( \(M_{2}^{ * }\) ) 30 and the Harmonic index ( \({HM}_{N}\) ) 31 for DDD networks. These topological indices are defined as \(F_{N}^{ * } = \sum\limits_{uv \in E\left( G \right)} {\left[ {\eta_{G} \left( u \right)^{2} + \eta_{G} \left( v \right)^{2} } \right]}\) , \(HM_{N} \left( G \right) = \sum\limits_{uv \in E\left( G \right)} {\left[ {\eta_{G} \left( u \right) + \eta_{G} \left( v \right)} \right]}^{2}\) , \(M_{2}^{ * } = \sum\limits_{uv \in E\left( G \right)} {\left[ {\eta_{G} \left( u \right) + \eta_{G} \left( v \right)} \right]}\) .

Constructions of dominating David derived networks (DDDN)

In the field of chemistry, honeycomb networks are utilized as representations for benzoid hydrocarbons. Honeycomb networks find extensive applications in various domains, including graphics, such as cell phone base stations and image processing. The honeycomb network is formed by enclosing the boundaries with a layer of hexagons. Based on the honeycomb network, different types of Dominating David derived networks can be derived. One can follow the below steps to construct the DDDN (t dimension):

Consider a t-dimension honeycomb network (see Fig.  1 a).

Add another vertex to divide each edge into two pieces (see Fig.  1 b).

In each hexagonal cell, connect the new vertices by an edge if they are at a distance of 4 within a hexagon (see Fig.  1 c).

Add new vertices at new edge intersections. (see Fig.  1 d).

Remove the starting vertices and edges of the honeycomb (see Fig.  1 e).

Divide each horizontal edge into two parts by addind a new vertex (see Fig.  1 f).

The steps to derive DDD (2).

Main results

Our key findings rely on the edge partitions of Figs.  2 , 3 and 4 as given below. We have calculated these edge partitions based on the degrees of the end vertices of each edge. For instance, the first row of Fig.  1 shows the degrees of the end vertices of edges, while the second row illustrates the count of edges with those specific degrees. In the same way, we have obtained the other tables.

First type of D 1 (2) network.

First type of D 2 (2) network.

Third type of D 3 (2) network.

The F N * topological index for dominating David derived networks

Let G be a graph in D 1 (t), D 2 (t) and D 3 (t) then according to the definition of \(F_{N}^{ * }\) and Table 1 , we have

Similarly, from Table 2 , we have

And from Table 3 , one has

The \({{\varvec{M}}}_{2}^{\boldsymbol{*}}\) topological index for DDDN

Let G be a graph in D 1 (t), D 2 (t) and D 3 (t) then according to the definition of \({M}_{2}^{*}\) and Table 1 we have

Likewise, based on the information presented in Table 2 , we obtain

The \({{\varvec{H}}{\varvec{M}}}_{{\varvec{N}}}\) topological index for DDDN

Let G be a graph in D 1 (t), D 2 (t) and D 3 (t) then according to the definition of \({HM}_{N}\) and Table 1 , we have

\(\begin{aligned} & HM_{N} \left( G \right) = 64t + 100t - 100 + 1008t - 576 + 324t^{2} - 468t + 180 + 1764t^{2} - 2744t + 1176 + 2304t^{2} - 3328t + 1280 \\ & HM_{N} \left( G \right) = 4392t^{2} - 5362t + 3240 \\ \end{aligned}\) Similarly, from Table 2 , we have

And from Table 3 , we have

Concluding Remarks

In this study, we have considered the \({F}_{N}^{*}\) , \({M}_{2}^{*}\) and \(HM_{N}\) topological indices. Our simulated results help for the better comprehend topology and enhance physical properties of the honeycomb structure. The computed indices, and above, as previously mentioned, have the most closely relates to the acentric factor and entropy consequently, they are extremely accurate in QSPR and QSAR analysis.

In Table 4 , the topological indices computed are represented mathematically. As we can see, increasing the values of t, increases the value of the indices as well. We have precise analytical formulations for the D 1 , D 2 and D 3 networks, considering various topological indices. In the rapidly expanding fields of nanotechnology and applications, such as networks, our current discoveries and techniques can be applied to other, more complex structures. The utilization of distance-based topological indices poses greater challenges and complexity, but they can be employed alongside existing methods. Exploring these types of studies will be the focus of future research endeavors. In Table 4 and Fig.  5 , we computed the numerical comparison of the certain topological indices for D 1 , D 2 and D 3 networks, which shows that when we increase t as a result the values of the topological indices also increases. These numerical comaprisons also shows that the inceasing rate of \(HM_{N}\) for D 3 is greater than the other topological indices. Since, in graph theory, the \(HM_{N}\) is a mathematical concept used to describe the connectivity. Therefore, a higher \(HM_{N}\) reflects the more connectivity among the atoms of a molecule. This indicates that the D 3 molecule has a greater potential for forming diverse interactions with other molecules and participating in a wider range of chemical reactions.

The comparison graph.

Data availability

All data generated or analysed during this study are included in this published article.

Zaman, S. et al. Mathematical analysis and molecular descriptors of two novel metal–organic models with chemical applications. Sci. Rep. 13 (1), 5314 (2023).

Article   ADS   CAS   PubMed   PubMed Central   Google Scholar  

Liu, H. Comparison between Merrifield–Simmons index and some vertex-degree-based topological indices. Comput. Appl. Math. 42 (2), 89 (2023).

Article   MathSciNet   MATH   Google Scholar  

Babar, U. et al. Multiplicative topological properties of graphs derived from honeycomb structure. Aims Math. 5 (2), 1562–1587 (2020).

Ali, H. et al. On the degree-based topological indices of some derived networks. Mathematics 7 (7), 612 (2019).

Article   Google Scholar  

Yang, S. et al. Structure of Fejes Tóth cells in natural honey bee combs. Apidologie 53 (1), 6 (2022).

Article   MathSciNet   Google Scholar  

Hayat, S., Malik, M. A. & Imran, M. Computing topological indices of honeycomb derived networks. Rom. J. Inf. Sci. Technol. 18 (2), 144–165 (2015).

Google Scholar  

Imran, M. et al. On topological properties of poly honeycomb networks. Period. Math. Hung. 73 , 100–119 (2016).

Mukwembi, S. & Nyabadza, F. A new model for predicting boiling points of alkanes. Sci. Rep. 11 (1), 24261 (2021).

Ahmad, M. S. et al. Calculating degree-based topological indices of dominating David derived networks. Open Phys. 15 (1), 1015–1021 (2017).

Imran, M., Baig, A. Q. & Ali, H. On topological properties of dominating David derived networks. Can. J. Chem. 94 (2), 137–148 (2016).

Article   CAS   Google Scholar  

Aslam, A. et al. On topological indices of certain dendrimer structures. Z. Naturforsch. A 72 (6), 559–566 (2017).

Article   ADS   CAS   Google Scholar  

Ullah, A., Zeb, A. & Zaman, S. A new perspective on the modeling and topological characterization of H-naphtalenic nanosheets with applications. J. Mol. Model. 28 (8), 1–13 (2022).

Wang, G. et al. The connective eccentricity index of graphs and its applications to octane isomers and benzenoid hydrocarbons. Int. J. Quantum Chem. 120 (18), e26334 (2020).

Mondal, S., De, N. & Pal, A. Topological properties of graphene using some novel neighborhood degree-based topological indices. Int. J. Math. Ind. 11 (01), 1950006 (2019).

De, N. et al. On some degree based topological indices of mk-graph. J. Discrete Math. Sci. Cryptogr. 23 (6), 1183–1194 (2020).

Zaman, S. & Ali, A. On connected graphs having the maximum connective eccentricity index. J. Appl. Math. Comput. 67 (1), 131–142 (2021).

Baig, A. Q., Imran, M. & Ali, H. On topological indices of poly oxide, poly silicate, DOX, and DSL networks. Can. J. Chem. 93 (7), 730–739 (2015).

Ullah, A. et al. Computational and comparative aspects of two carbon nanosheets with respect to some novel topological indices. Ain Shams Eng. J. 13 (4), 101672 (2022).

Javaid, M., Rehman, M. U. & Cao, J. Topological indices of rhombus type silicate and oxide networks. Can. J. Chem. 95 (2), 134–143 (2017).

Koam, A. N. et al. Entropy measures of Y-junction based nanostructures. Ain Shams Eng. J. 2022 , 10 (1913).

Ahmad, A. & Imran, M. J. C. Vertex-edge-degree-based topological properties for hex-derived networks. Complexity 2022 , 1–13 (2022).

ADS   Google Scholar  

Ahmad, A. et al. Analysis of distance-based topological polynomials associated with zero-divisor graphs. Comput. Mater. Contin. 70 (2), 2898–2904 (2022).

Ahmad, A. et al. Polynomials of degree-based indices of metal-organic networks. Comb. Chem. High Throughput Screen. 25 (3), 510–518 (2022).

Article   CAS   PubMed   Google Scholar  

Zaman, S., et al., The Kemeny’s Constant and Spanning Trees of Hexagonal Ring Network.

Khabyah, A. A. et al. Minimum zagreb eccentricity indices of two-mode network with applications in boiling point and benzenoid hydrocarbons. Mathematics 10 (9), 1393 (2022).

Zaman, S. et al. Maximum H-index of bipartite network with some given parameters. AIMS Math. 6 (5), 5165–5175 (2021).

Zaman, S. Cacti with maximal general sum-connectivity index. J. Appl. Math. Comput. 65 (1), 147–160 (2021).

Zaman, S. Spectral analysis of three invariants associated to random walks on rounded networks with 2 n-pentagons. Int. J. Comput. Math. 99 (3), 465–485 (2022).

Gao, W. et al. Forgotten topological index of chemical structure in drugs. Saudi Pharm. J. 24 (3), 258–264 (2016).

Article   PubMed   PubMed Central   Google Scholar  

Khalifeh, M., Yousefi-Azari, H. & Ashrafi, A. R. The first and second zagreb indices of some graph operations. Discrete Appl. Math. 157 (4), 804–811 (2009).

Zhong, L. The harmonic index for graphs. Appl. Math. Lett. 25 (3), 561–566 (2012).

Download references

Author information

Authors and affiliations.

Department of Mathematics, University of Sialkot, Sialkot, 51310, Pakistan

Shahid Zaman, Wakeel Ahmed & Atash Sakeena

Faculity of Science, University of Zakho, Duhok, Kurdistan Region, Iraq

Kavi Bahri Rasool

Department of Mathematics, Wollega University, 395, Nekemte, Ethiopia

Mamo Abebe Ashebo

You can also search for this author in PubMed   Google Scholar

Contributions

All authors have made equal contributions to this paper at every stage, including conceptualization and the final drafting process. The manuscript has been approved by all authors and consent for publication has been granted.

Corresponding author

Correspondence to Mamo Abebe Ashebo .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Cite this article.

Zaman, S., Ahmed, W., Sakeena, A. et al. Mathematical modeling and topological graph description of dominating David derived networks based on edge partitions. Sci Rep 13 , 15159 (2023). https://doi.org/10.1038/s41598-023-42340-6

Download citation

Received : 06 June 2023

Accepted : 08 September 2023

Published : 13 September 2023

DOI : https://doi.org/10.1038/s41598-023-42340-6

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

This article is cited by

Reduced reverse degree-based topological indices of graphyne and graphdiyne nanoribbons with applications in chemical analysis.

• Shahid Zaman
• K. H. Hakami
• Fekadu Tesgera Agama

Scientific Reports (2024)

By submitting a comment you agree to abide by our Terms and Community Guidelines . If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Sign up for the Nature Briefing: AI and Robotics newsletter — what matters in AI and robotics research, free to your inbox weekly.

Grab your spot at the free arXiv Accessibility Forum

Help | Advanced Search

Mathematics > Statistics Theory

Title: spectral graph analysis: a unified explanation and modern perspectives.

Abstract: Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful techniques and models for understanding `patterns of interconnectedness' in a graph. Our prime focus in this paper is on the following question: Is there a unified explanation and description of the fundamental spectral graph methods? There are at least two reasons to be interested in this question. Firstly, to gain a much deeper and refined understanding of the basic foundational principles, and secondly, to derive rich consequences with practical significance for algorithm design. However, despite half a century of research, this question remains one of the most formidable open issues, if not the core problem in modern network science. The achievement of this paper is to take a step towards answering this question by discovering a simple, yet universal statistical logic of spectral graph analysis. The prescribed viewpoint appears to be good enough to accommodate almost all existing spectral graph techniques as a consequence of just one single formalism and algorithm.

Submission history

Access paper:.

• Other Formats

References & Citations

• Google Scholar
• Semantic Scholar

BibTeX formatted citation

Bibliographic and Citation Tools

Code, data and media associated with this article, recommenders and search tools.

• Institution

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

Information

• Author Services

Initiatives

You are accessing a machine-readable page. In order to be human-readable, please install an RSS reader.

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited. For more information, please refer to https://www.mdpi.com/openaccess .

Feature papers represent the most advanced research with significant potential for high impact in the field. A Feature Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for future research directions and describes possible research applications.

Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive positive feedback from the reviewers.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

Original Submission Date Received: .

• Active Journals
• Find a Journal
• Proceedings Series
• For Authors
• For Reviewers
• For Editors
• For Librarians
• For Publishers
• For Societies
• For Conference Organizers
• Open Access Policy
• Institutional Open Access Program
• Special Issues Guidelines
• Editorial Process
• Research and Publication Ethics
• Article Processing Charges
• Testimonials
• Preprints.org
• SciProfiles
• Encyclopedia

Journal Menu

• Mathematics Home
• Aims & Scope
• Editorial Board
• Reviewer Board
• Topical Advisory Panel
• Instructions for Authors
• Special Issues
• Sections & Collections
• Article Processing Charge
• Indexing & Archiving
• Editor’s Choice Articles
• Most Cited & Viewed
• Journal Statistics
• Journal History
• Journal Awards
• Society Collaborations
• Conferences
• Editorial Office

Journal Browser

• arrow_forward_ios Forthcoming issue arrow_forward_ios Current issue
• Vol. 12 (2024)
• Vol. 11 (2023)
• Vol. 10 (2022)
• Vol. 9 (2021)
• Vol. 8 (2020)
• Vol. 7 (2019)
• Vol. 6 (2018)
• Vol. 5 (2017)
• Vol. 4 (2016)
• Vol. 3 (2015)
• Vol. 2 (2014)
• Vol. 1 (2013)

Find support for a specific problem in the support section of our website.

Please let us know what you think of our products and services.

Visit our dedicated information section to learn more about MDPI.

Recent Advances in Chemical Graph Theory and Their Applications

Special issue editors, special issue information, benefits of publishing in a special issue.

• Published Papers

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section " Network Science ".

Deadline for manuscript submissions: closed (31 January 2021) | Viewed by 22988

Share This Special Issue

Dear Colleagues,

Since the seminal paper of the American chemist Harold Wiener in 1947, many numerical quantities of graphs have been introduced and extensively studied in order to describe various physicochemical properties. Such graph invariants are most commonly referred to as topological indices and are often defined using degrees of vertices, distances between vertices, eigenvalues, symmetries, and many other properties of graphs. It is desirable for a topological index to also be a molecular descriptor. In order to establish the connection between topological indices and the properties or activities of studied compounds, quantitative structure–activity relationships (QSAR) and quantitative structure–property relationships (QSPR) must be performed. This enables the process of finding new compounds with desired properties in silico instead of in vitro.

There are well studied groups of molecules composed of carbon and hydrogen atoms, but modeling of more complex heteroatomic compounds is much more challenging. On the other hand, topological indices have also found enormous applications in rapidly growing research of complex networks, which include communications networks, social networks, biological networks, etc. In such networks, these indices are used as measures for various structural properties.

The purpose of this Special Issue is to report and review recent developments concerning mathematical properties, methods of calculations, and applications of topological indices in any area of interest. Moreover, papers on other topics in chemical graph theory are also welcome.

Prof. Dr. Petra Zigert Pletersek Dr. Niko Tratnik Guest Editors

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website . Once you are registered, click here to go to the submission form . Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• Topological indices
• Molecular descriptors
• Methods of calculations
• QSP(A)R analysis
• Molecular graphs
• Complex molecules
• Nanostructures
• Different measures in networks
• Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
• Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
• Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
• External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
• e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here .

Published Papers (5 papers)

Graphical abstract

Further Information

Mdpi initiatives, follow mdpi.

Subscribe to receive issue release notifications and newsletters from MDPI journals

Spectral Graph Theory - Science topic

• Recruit researchers
• Join for free
• Login Email Tip: Most researchers use their institutional email address as their ResearchGate login Password Forgot password? Keep me logged in Log in or Continue with Google Welcome back! Please log in. Email · Hint Tip: Most researchers use their institutional email address as their ResearchGate login Password Forgot password? Keep me logged in Log in or Continue with Google No account? Sign up