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

Alaa Altassan, Anwar Saleh (), Marwa Hamed and Najat Muthana ()
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Alaa Altassan: Department of Mathematics, College of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Anwar Saleh: Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21589, Saudi Arabia
Marwa Hamed: Department of Mathematics, College of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Najat Muthana: Department of Mathematics, College of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2024, vol. 12, issue 13, 1-23

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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