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Volume 12
Issue 13
10.3390/math12132126
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Characterizing Finite Groups through Equitable Graphs: A Graph-Theoretic Approach

by
Alaa Altassan
1,
Anwar Saleh
2,*,
Marwa Hamed
1 and
Najat Muthana
1,*
1
Department of Mathematics, College of Science, King Abdul Aziz University, Jeddah 21589, Saudi Arabia
2
Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21589, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Mathematics 2024, 12(13), 2126; https://doi.org/10.3390/math12132126 (registering DOI)
Submission received: 2 May 2024 / Revised: 3 July 2024 / Accepted: 5 July 2024 / Published: 6 July 2024
(This article belongs to the Special Issue Algebraic Structures and Graph Theory, 2nd Edition)
Versions Notes

Abstract

This paper introduces equitable graphs of Type I associated with finite groups. We investigate the connectedness and some graph-theoretic properties of these graphs for various groups. Furthermore, we establish the novel concepts of the equitable square-free number and the equitable group. Our study includes an analysis of the equitable graphs for specific equitable groups. Additionally, we determine the first, second and forgotten Zagreb topological indices for the equitable graphs of Type I constructed from certain groups. Finally, we derive the adjacency matrix for this graph type built from cyclic p-groups.
Keywords: equitable graph; equitable group; topological indices equitable graph; equitable group; topological indices

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MDPI and ACS Style

Altassan, A.; Saleh, A.; Hamed, M.; Muthana, N. Characterizing Finite Groups through Equitable Graphs: A Graph-Theoretic Approach. Mathematics 2024, 12, 2126. https://doi.org/10.3390/math12132126

AMA Style

Altassan A, Saleh A, Hamed M, Muthana N. Characterizing Finite Groups through Equitable Graphs: A Graph-Theoretic Approach. Mathematics. 2024; 12(13):2126. https://doi.org/10.3390/math12132126

Chicago/Turabian Style

Altassan, Alaa, Anwar Saleh, Marwa Hamed, and Najat Muthana. 2024. "Characterizing Finite Groups through Equitable Graphs: A Graph-Theoretic Approach" Mathematics 12, no. 13: 2126. https://doi.org/10.3390/math12132126

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