“School of Mathematics”
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Paper IPM / M / 11534  


Abstract:  
Let G be a nonabelian group. We define the
noncommuting graph ∇(G) of G as follows: its vertex set
is G\Z(G), the set of noncentral elements of G, and
two different vertices x and y are joined by an edge if and
only if x and y do not commute as elements of G, i.e.,
[x,y] ≠ 1. We prove that if L ∈ {L_{4}(7), L_{4}(11), L_{4}(13), L_{4}(16), L_{4}(17)} and G is a finite group such that
∇(G) ≅ ∇(L), then G ≅ L.
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