Chromatic number and clique number of subgraphs of regular graph of matrix algebras

Akbari, S.; Aryapoor, Masood; Jamaali, M.

doi:10.1016/j.laa.2011.09.020

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Cited by 13 publications

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“…The graph Γ(M n (F)), which we shall denote by Γ n (F) for simplicity, was studied in [2] and [1]. Akbari, Jamaali, Fakhari [2] proved that…”

Section: Introductionmentioning

confidence: 99%

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On the chromatic number of regular graphs of matrix algebras

Tomon

2015

Linear Algebra and its Applications

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Let R be a ring and Z(R) be the set of zero divisors of R. The regular graph of R, denoted by Γ(R) is the graph with vertex set R\Z(R) and {X, Y } is an edge if X +Y ∈ Z(R). We prove that the chromatic number of Γ(M n (F q )) is at least (q/4) n/2 , where M n (F q ) is the ring of n × n matrices over F q , q being an odd prime power. This proves that the chromatic number of Γ(M n (F alg p )) is infinite, answering a case of a question posed in BCC22.

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“…The graph Γ(M n (F)), which we shall denote by Γ n (F) for simplicity, was studied in [2] and [1]. Akbari, Jamaali, Fakhari [2] proved that…”

Section: Introductionmentioning

confidence: 99%

“…Akbari, Aryapoor and Jamaali [1] established that certain subgraphs of Γ n (F) have finite chromatic number. In their paper, they also proved the following result (Corollary 3. in [1] …”

Section: Introductionmentioning

confidence: 99%