Advances in Graph Theory and Combinatorics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 30 October 2026 | Viewed by 624

Editor

School of Software, South China Normal University, Foshan 528225, China
Interests: graph theory; discrete mathematics; combinatorics; matrix theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Graph theory and combinatorics continue to play a foundational role across mathematics, computer science, and other applied sciences. This Special Issue, titled “Advances in Graph Theory and Combinatorics”, seeks to highlight recent progress and emerging directions in these dynamic and deeply interconnected areas of discrete mathematics. It aims to bring together high-quality contributions that expand theoretical understanding, introduce innovative techniques, or demonstrate impactful applications.

We invite submissions that present new theoretical breakthroughs, refined or novel methodologies, powerful structural or algebraic insights, or significant applications to related disciplines. Original research articles that contribute to any area of graph theory or combinatorics are welcome.

Topics of interest include, but are not limited to, the following:

  • Structural graph theory, extremal graph theory, and extremal combinatorics;
  • Algebraic, analytic, and topological methods in graph theory and combinatorics;
  • Probabilistic techniques, random graphs, and probabilistic combinatorics;
  • Algorithmic and computational aspects of graph theory and combinatorial optimization;
  • Enumerative combinatorics, generating function techniques, and bijective methods;
  • Graph invariants and eigenvalue problems, including applications of spectral graph theory;
  • Combinatorial structures in geometry, number theory, and algebra;
  • Applications to networks, theoretical computer science, information theory, biology, chemistry, and statistical physics;
  • Emerging interdisciplinary directions, including complex networks, data science, and discrete models in the physical and life sciences.

This Special Issue aims to serve as a forum for the dissemination of influential contributions that deepen our understanding of discrete structures, stimulate cross-disciplinary dialogue, and inspire future research.

Dr. Zhibin Du
Guest Editor

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Keywords

  • graph theory
  • combinatorics
  • discrete mathematics
  • extremal problems
  • algebraic combinatorics
  • spectral graph theory
  • probabilistic methods
  • algorithmic graph theory
  • enumerative combinatorics
  • network science
  • random graphs
  • combinatorial optimization

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Published Papers (1 paper)

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Research

16 pages, 308 KB  
Article
Reciprocal Mean Square Index of Graphs
by Abdulaziz Mutlaq Alotaibi and Akbar Ali
Mathematics 2026, 14(15), 2830; https://doi.org/10.3390/math14152830 - 5 Aug 2026
Viewed by 131
Abstract
The reciprocal mean square (RMS) index of a graph G with edge set E(G) is defined by [...] Read more.
The reciprocal mean square (RMS) index of a graph G with edge set E(G) is defined by RMS(G)=uvE(G)[(d(u))2+(d(v))2]1, where d(u) and d(v) are the degrees of vertices u and v, respectively. We first establish several bounds for the RMS index in terms of standard graph parameters (including the size, minimum degree, and maximum degree) and related degree-based indices, such as the forgotten index, the Sombor index, the reciprocal hyper-Zagreb index, the inverse degree index, and the harmonic index. We then determine the extremal values of the RMS index over the classes of n-order trees and unicyclic graphs for n3. For n-order trees, the path Pn and the star Sn are the extremal graphs for the considered index, as expected. However, for unicyclic graphs of sufficiently large order, the graph minimizing the RMS index is, rather surprisingly, not the one containing a universal vertex. This indicates that the extremal behavior of the RMS index may differ from that of many existing degree-based indices. Full article
(This article belongs to the Special Issue Advances in Graph Theory and Combinatorics)
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