Enhanced Power Graph of Certain Non-abelian Groups
Group Theory
2021-08-31 v1 Combinatorics
Abstract
The enhanced power graph of a group is a simple undirected graph with vertex set 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.
Cite
@article{arxiv.2108.13006,
title = {Enhanced Power Graph of Certain Non-abelian Groups},
author = {Parveen and Sandeep Dalal and Jitender Kumar},
journal= {arXiv preprint arXiv:2108.13006},
year = {2021}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2008.07098