On enhanced power graphs of certain groups

Abstract

The enhanced power graph Pe(G) of a group G is a simple undirected graph with vertex set G and two distinct vertices x,y are adjacent if both x and y belongs to same cyclic subgroup of G. In this paper, we obtain various graph invariants viz. independence number, minimum degree and matching number of Pe(G), where G is the dicyclic group or a class of groups of order 8n. If G is any of these groups, we prove that Pe(G) is perfect and then obtain its strong metric dimension.