K3,3-free intersection graphs of finite groups

Abstract

ABSTRACTThe intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if H∩K≠1 where 1 denotes the trivial subgroup of G. In this paper we classify all finite groups whose intersection graphs are K3,3-free.