On enhanced power graphs of certain groups

Abstract

The enhanced power graph [Formula: see text] of a group [Formula: see text] is a simple undirected graph with vertex set [Formula: see text] and two distinct vertices [Formula: see text] are adjacent if both [Formula: see text] and [Formula: see text] belongs to same cyclic subgroup of [Formula: see text]. In this paper, we obtain various graph invariants viz. independence number, minimum degree and matching number of [Formula: see text], where [Formula: see text] is the dicyclic group or a class of groups of order [Formula: see text]. If [Formula: see text] is any of these groups, we prove that [Formula: see text] is perfect and then obtain its strong metric dimension.