A Note on Integral Non-Commuting Graphs

Modjtaba Ghorbani, Zahra Gharavi-Alkhansari


The non-commuting graph Γ(G) of group G is a graph with the vertex set
G − Z(G) and two distinct vertices x and y are adjacent whenever xy ̸= yx. In
this paper, we compute the spectrum of non-commuting graphs of some wellknown
groups. Further, if G is a non-abelian finite group and its non-commuting
graph Γ(G) is k−regular, then we prove k ̸= 2sq where q is an odd prime.

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