Topological Analysis and Computation of Chemical Graphs and Physical Networks

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 20 October 2025 | Viewed by 1574

Special Issue Editors


E-Mail Website
Guest Editor
School of Science, China University of Geosciences (Beijing), Beijing 100083, China
Interests: graph theory; combinatorics; complex networks; applied statistics and algorithms

E-Mail Website
Guest Editor
Department of Mathematics, Louisiana Christian University, Pineville, LA 71359, USA
Interests: graph theory; applied mathematics and computation

Special Issue Information

Dear Colleagues,

With the rapid development of chemical and physical technologies, increasingly more new practical problems have rapidly emerged, bringing challenges to the topological analysis and computation of graphs and networks. Consequently, the topological analysis and computation of chemical graphs and physical networks have become common and indispensable in tackling problems in both the academic and practical fields.

Specifically, the aim of this Research Topic is to provide a general view of the current research in the topological analysis and computation of chemical graphs and physical networks, as well as to show how mathematics can help in such important aspects as understanding, analysis, computation, prediction, treatment, and data processing.

We encourage the submissions of theoretical as well as applied investigations on methods for the topological analysis and computation of chemical graphs and physical networks based on their parameters such as topological indices, graph labeling, metric dimensions, entropy, and energies.

Potential topics include but are not limited to the following:

  • Crossing-study of Graph Theory and Artificial Intelligence Algorithm;
  • Topological analysis of chemical graphs and physical networks;
  • Computation of topological indices, energies, metric dimensions, and the entropy of chemical graphs and physical networks;
  • Mathematical modeling in chemical graphs and physical networks;
  • Different labelings of chemical graphs and physical networks;
  • Mathematical calculation of complex networks;
  • Algorithm analysis on chemical graphs and physical networks.

Prof. Dr. Haiying Wang
Dr. Shaohui Wang
Guest Editors

Manuscript Submission Information

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.

Keywords

  • chemical indices
  • labeling
  • topological analysis and computation
  • algorithms
  • molecular graphs
  • complex networks

Benefits of Publishing in a Special Issue

  • 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.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (2 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

16 pages, 3824 KiB  
Article
Style Transfer and Topological Feature Analysis of Text-Based CAPTCHA via Generative Adversarial Networks
by Tao Xue, Zixuan Guo, Zehang Yin and Yu Rong
Mathematics 2025, 13(11), 1861; https://doi.org/10.3390/math13111861 - 2 Jun 2025
Viewed by 248
Abstract
The design and cracking of text-based CAPTCHAs are important topics in computer security. This study proposes a method for the style transfer of text-based CAPTCHAs using Generative Adversarial Networks (GANs). First, a curated dataset was used, combining a text-based CAPTCHA library and image [...] Read more.
The design and cracking of text-based CAPTCHAs are important topics in computer security. This study proposes a method for the style transfer of text-based CAPTCHAs using Generative Adversarial Networks (GANs). First, a curated dataset was used, combining a text-based CAPTCHA library and image collections from four artistic styles—Van Gogh, Monet, Cézanne, and Ukiyo-e—which were used to generate style-based text CAPTCHA samples. Subsequently, a universal style transfer model, along with trained CycleGAN models for both single- and double-style transfers, were employed to generate style-enhanced text-based CAPTCHAs. Traditional methods for evaluating the anti-recognition capability of text-based CAPTCHAs primarily focus on recognition success rates. This study introduces topological feature analysis as a new method for evaluating text-based CAPTCHAs. Initially, the recognition success rates of the three methods across four styles were evaluated using Muggle-OCR. Subsequently, the graph diameter was employed to quantify the differences between text-based CAPTCHA images before and after style transfer. The experimental results demonstrate that the recognition rates of style-enhanced text-based CAPTCHAs are consistently lower than those of the original CAPTCHA, suggesting that style transfer enhances anti-recognition capability. Topological feature analysis indicates that style transfer results in a more compact topological structure, further validating the effectiveness of the GAN-based twice-transfer method in enhancing CAPTCHA complexity and anti-recognition capability. Full article
Show Figures

Figure 1

13 pages, 319 KiB  
Article
Zagreb Root-Indices of Graphs with Chemical Applications
by Niko Tratnik and Petra Žigert Pleteršek
Mathematics 2024, 12(23), 3871; https://doi.org/10.3390/math12233871 - 9 Dec 2024
Viewed by 763
Abstract
Root-indices of graphs are mathematical tools that help us to understand complex systems, like molecules and networks, by capturing key structural information. In this study, we introduce two new root-indices, the first and the second Zagreb root-index, and we analyze their properties. We [...] Read more.
Root-indices of graphs are mathematical tools that help us to understand complex systems, like molecules and networks, by capturing key structural information. In this study, we introduce two new root-indices, the first and the second Zagreb root-index, and we analyze their properties. We apply these indices to chemical structures like benzenoid molecules and octane isomers, showing that they sometimes provide better insights than traditional indices. We also compare the effectiveness of several root-indices with their standard versions, highlighting their ability to distinguish between different graph structures. Full article
Show Figures

Figure 1

Back to TopTop