Common Divisor Graph of Finite Groups

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DOI: https://doi.org/10.28924/2291-8639-23-2025-89
Published: Apr 14, 2025
Cite as:
Nasr Zeyada, Anwar Saleh, Marwan Alsubhi, Common Divisor Graph of Finite Groups, Int. J. Anal. Appl., 23 (2025), 89.

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Nasr Zeyada, Anwar Saleh, Marwan Alsubhi

Abstract

The interaction between groups and graphs is the most popular and gainful area of algebraic graph theory. We introduce and scrutinize a graph whose vertex set is a group $H$ and the vertices $a$ and $b$ with different orders are adjacent if \(c\notin \{e,a,b\}\) exists such that \(|c| | (|a|, |b|)\) or only one of \(a\) or \(b\) is the identity. We investigate this graph by presenting various examples and demonstrating some important properties and results.

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