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 294

Special Issue Editors


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Guest Editor
Department of Engineering, Universidad Loyola, Sevilla, Spain
Interests: non-associative algebras; graph theory; evolution algebras; combinatorial structures; (pseudo)digraphs; algorithms

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Guest Editor
Department of Applied Mathematics I, University of Seville, 41012 Sevilla, Spain
Interests: discrete mathematics; graph theory; combinatorics; computational geometry; Latin squares
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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

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Keywords

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

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Published Papers (1 paper)

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Research

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 136
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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