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Mathematics
Special Issues
Graph Theory and Its Applications 2025
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Graph Theory and Its Applications 2025

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

Deadline for manuscript submissions: closed (31 August 2025) | Viewed by 1731

Special Issue Editor

Dr. Arash Rafiey

E-Mail Website
Guest Editor
Department of Math and Computer Science, Indiana State University, 200 N 7th Street, Terre Haute, IN 47809, USA
Interests: algorithmic graph theory; constraint satisfaction problems; approximation algorithms; operation research

Special Issue Information

Dear Colleagues,

We would like to invite you to submit your recent research on graph theory, algorithmic graph theory, and their applications in other fields to this Special Issue, entitled “Graph Theory and Its Applications 2025”. Graph theory has various applications in diverse fields, including computer science, social networks, biology, telecommunications, transportation, and operation research, and we especially encourage research papers broadening its reach.

The scope of this Special Issue includes, but is not limited to, the following:

  • Algorithmic graph theory (including the approximation algorithm and the fixed parameterised algorithm);
  • Structural graph theory;
  • Combinatorial optimisation and mathematical modelling;
  • Computational applications of graph theory (including bioinformatics and computer search in graph theory);
  • Graph mining and knowledge discovery;
  • Machine learning algorithms inspired by graph theory concepts.

Dr. Arash Rafiey
Guest Editor

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

  • algorithmic graph theory
  • structural graph theory
  • forbidden obstructions
  • approximation algorithm
  • graph classes
  • pattern recognition
  • graph search

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

Published Papers (2 papers)

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Research

25 pages, 402 KB  
Article
Prime Graphs with Almost True Twin Vertices
by Aymen Ben Amira and Moncef Bouaziz
Mathematics 2025, 13(21), 3466; https://doi.org/10.3390/math13213466 (registering DOI) - 30 Oct 2025
Abstract
A graph G consists of a possibly infinite set V(G) of vertices with a collection E(G) of unordered pairs of distinct vertices, called the set of edges of G. Such a graph is denoted by [...] Read more.
A graph G consists of a possibly infinite set V(G) of vertices with a collection E(G) of unordered pairs of distinct vertices, called the set of edges of G. Such a graph is denoted by (V(G),E(G)). Two distinct vertices u and v of a graph G are adjacent if {u,v}∈E(G). Let G be a graph. A subset M of V(G) is a module of G if every vertex outside M is adjacent to all or none of the vertices in M. The graph G is prime if it has at least four vertices, and its only modules are ∅, the single-vertex sets, and V(G). Given two adjacent vertices u and v of G, v is a negative almost true twin of u in G if there is a vertex xv in V(G)∖{u} non-adjacent to u such that the pair {u,v} is a module of the graph (V(G),E(G)∪{{u,xv}}). In this paper, we study graphs with a negative almost true twin for a given vertex, and we give some applications. Firstly, we characterize these graphs by a special decomposition, and we specify the prime graphs among them. Secondly, we give three applications, giving methods for extending graphs to prime graphs. Finally, we study the prime induced subgraphs of the prime graphs with at least two negative almost true twins for a given vertex. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications 2025)
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13 pages, 268 KB  
Article
Vertex–Edge Roman {2}-Domination
by Ahlam Almulhim and Saiful Rahman Mondal
Mathematics 2025, 13(13), 2169; https://doi.org/10.3390/math13132169 - 2 Jul 2025
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Abstract
A vertex–edge Roman {2}-dominating function on a graph G=(V,E) is a function f:V⟶{0,1,2} satisfying that, for every edge uv∈E with [...] Read more.
A vertex–edge Roman {2}-dominating function on a graph G=(V,E) is a function f:V⟶{0,1,2} satisfying that, for every edge uv∈E with f(v)=f(u)=0, ∑w∈N(v)∪N(u)f(w)≥2. The weight of the function f is the sum ∑a∈Vf(a). The vertex–edge Roman {2}-domination number of G, denoted by γveR2(G), is the minimum weight of a vertex–edge Roman {2}-dominating function on G. In this work, we begin the study of vertex–edge Roman {2}-domination. We determine the exact vertex–edge Roman {2}-domination number for cycles and paths, and we provide a tight lower bound and a tight upper bound for the vertex–edge Roman {2}-domination number of trees. In addition, we prove that the decision problem associated with vertex–edge Roman {2}-domination is NP-complete for bipartite graphs. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications 2025)
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