Non - commuting graph of a group ✩
نویسندگان
چکیده
Let G be a non-abelian group and let Z(G) be the center of G. Associate a graph ΓG (called noncommuting graph of G) with G as follows: Take G\Z(G) as the vertices of ΓG and join two distinct vertices x and y, whenever xy = yx. We want to explore how the graph theoretical properties of ΓG can effect on the group theoretical properties of G. We conjecture that if G and H are two non-abelian finite groups such that ΓG ∼= ΓH , then |G| = |H |. Among other results we show that if G is a finite non-abelian nilpotent group and H is a group such that ΓG ∼= ΓH and |G| = |H |, then H is nilpotent. 2006 Elsevier Inc. All rights reserved.
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