Lower Bounds and Maximal Clique Structure in Matrix Commuting Graphs

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DOI: https://doi.org/10.28924/2291-8639-24-2026-252
Published: Aug 17, 2026
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Manal Al-Labadi, Lower Bounds and Maximal Clique Structure in Matrix Commuting Graphs, Int. J. Anal. Appl., 24 (2026), 252.

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Manal Al-Labadi

Abstract

Let \(R\) be a finite commutative ring with unity and let \(M(m, R)\) denote the ring of \(m \times m\) matrices over \(R\). We investigate the commuting graph \(\Gamma(M(m, R))\) whose vertices are the non-central matrices in \(M(m, R)\) and two distinct vertices are adjacent if and only if they commute. In this paper, we establish the lower bound of the clique number \(\omega(\Gamma(M(m, R)))\). Our main results we characterize the structure of maximal cliques.

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