• OPERATOR INTERSECTION GRAPH OF A GROUP
Abstract
Let (G, ∗) be a group with binary operation ‘∗′. The Operator Intersection graph ΓOI(G) of G is a graph with V (ΓOI(G)) = G – e and two distinct vertices x and y are adjacent in ΓOI(G) if and only if <x∗y>⊆<x>∩ < y >. In this paper, we want to explore how the group theoretical properties of G can effect on the graph theoretical properties of ΓOI(G). Some characterizations for fundamental properties of ΓOI(G) have also been obtained. Finally, we characterize certain classes of Operator Intersection Graph corresponding to finite abelian groups.
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