On the noncommuting graph associated with a finite group
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Let G be a finite group. We define the noncommuting graph ∇(G) as follows: the vertex set of ∇(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. We study some properties of ∇(G) and prove that, for many groups G, if H is a group with ∇(G) isomorphic to ∇(H) then |G| = |H|.
Keywordsgroup noncommuting graph regular graph
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