Finite groups with regular join graph of subgroups

摘要

Let G be a non-trivial finite group different from a cyclic p-group. The join graph of G is a graph whose vertex set is the set of all proper subgroups of G which are not contained in the Frattini subgroup of G and two distinct vertices H and K are joined by an edge if and only if G = < H, K >. In this paper we classify finite groups with regular graphs and determine their graphs.