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Axioms
Special Issues
Advances in Graph Theory with Its Applications
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Advances in Graph Theory with Its Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 July 2025 | Viewed by 360

Special Issue Editors

Dr. Manuel Ceballos

E-Mail Website
Guest Editor
Department of Engineering, Universidad Loyola, Sevilla, Spain
Interests: non-associative algebras; graph theory; evolution algebras; combinatorial structures; (pseudo)digraphs; algorithms
Dr. Raúl M. Falcón

E-Mail Website
Guest Editor
Department of Applied Mathematics I, University of Seville, 41012 Sevilla, Spain
Interests: discrete mathematics; graph theory; combinatorics; computational geometry; Latin squares
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Graph theory, a cornerstone of discrete mathematics, has continually evolved as a powerful tool to model and solve problems across diverse domains. From analyzing complex networks in computer science and communication systems to optimizing processes in logistics, biology, and social sciences, its applications are both vast and impactful.

This Special Issue, "Advances in Graph Theory with Its Applications", aims to highlight recent developments in theoretical graph concepts, algorithmic innovations, and real-world implementations. Topics of interest include, but are not limited to, advancements in graph algorithms, structural graph properties, computational geometry, and their interdisciplinary applications in areas such as data science, energy systems, and network analysis.

We invite contributions that bridge the gap between theory and practice, offering novel insights or innovative methodologies that enhance our understanding of graph theory's capabilities. By fostering this dialogue, we hope to provide a platform for researchers to showcase the potential of graph theory approaches in addressing contemporary challenges.

Dr. Manuel Ceballos
Dr. Raúl M. Falcón
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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • graph theory
  • graph algorithms
  • network analysis
  • structural graph properties
  • computational geometry
  • graph applications
  • interdisciplinary mathematics
  • optimization
  • modeling

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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

20 pages, 301 KiB  
Article
Exploring the Structural and Traversal Properties of Total Graphs over Finite Rings
by Ali Al Khabyah, Nazim and Ikram Ali
Axioms 2025, 14(5), 386; https://doi.org/10.3390/axioms14050386 - 20 May 2025
Abstract
This paper extends the concept of the total graph TΓ(R) associated with a commutative ring to the three-fold Cartesian product R=Zn×Zm×Zp, where n,m,p>1 [...] Read more.
This paper extends the concept of the total graph TΓ(R) associated with a commutative ring to the three-fold Cartesian product R=Zn×Zm×Zp, where n,m,p>1. We present complete and self-contained proofs for a wide range of graph-theoretic properties of TΓ(R), including connectivity, diameter, regularity conditions, clique and independence numbers, and exact criteria for Hamiltonicity and Eulericity. We also derive improved lower bounds for the genus and characterize the automorphism group in both general and symmetric cases. Each result is illustrated through concrete numerical examples for clarity. Beyond theoretical contributions, we discuss potential applications in cryptographic key-exchange systems, fault-tolerant network architectures, and algebraic code design. This work generalizes and deepens prior studies on two-factor total graphs, and establishes a foundational framework for future exploration of higher-dimensional total graphs over finite commutative rings. Full article
(This article belongs to the Special Issue Advances in Graph Theory with Its Applications)
13 pages, 547 KiB  
Article
When Every Total Program Is a Finite Tree-Program: A Study of Program-Saturated Classes of Structures
by Mikhail Moshkov
Axioms 2025, 14(4), 307; https://doi.org/10.3390/axioms14040307 - 17 Apr 2025
Viewed by 166
Abstract
This paper investigates classes of structures and individual structures where programs implementing functions defined everywhere (total programs) are equivalent to finite tree-programs. The programs considered may include cycles and contain at most countably many nodes. The analysis begins with programs where arbitrary terms [...] Read more.
This paper investigates classes of structures and individual structures where programs implementing functions defined everywhere (total programs) are equivalent to finite tree-programs. The programs considered may include cycles and contain at most countably many nodes. The analysis begins with programs where arbitrary terms of a given signature are used in function nodes, and arbitrary formulas of this signature are used in predicate nodes. The results are then extended to programs that closely resemble computation trees: if such a program is a finite tree-program, it can be classified as an ordinary computation tree. Full article
(This article belongs to the Special Issue Advances in Graph Theory with Its Applications)
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