Enhanced Power Graph of Certain Non-abelian Groups

Abstract

The enhanced power graph of a group $G$ is a simple undirected graph with vertex set $G$ and two vertices are adjacent if they belong to same cyclic subgroup. In this paper, we study distant properties and detour distant properties such as closure, interior, distance degree sequence and eccentric subgraph of the enhanced power graph of semidihedral group. Consequently, we obtained the metric dimension and resolving polynomial of the enhanced power graph of semidihedral group. At the final part of this paper, we obtained the Laplacian spectrum of the enhanced power graph of semidihedral, dihedral and generalized quaternion groups.

arXiv admin note: substantial text overlap with arXiv:2008.07098

References in corpus (2)

• The rainbow connection number of enhanced power graph
• The enhanced quotient graph of the quotient of a finite group