2022/07/11 by Parveen, Jitender Kumar, Kumar, Jitender +4
Mathematics · Physics and Astronomy · #Graph theory and applications #Finite Group Theory Research #Semiconductor materials and interfaces
paper · pdf · doi:10.48550/arxiv.2207.05075
The enhanced power graph of a finite group G, denoted by PE(G), is the simple undirected graph whose vertex set is G and two distinct vertices x, y are adjacent if x, y ∈ ⟨ z ⟩ for some z ∈ G. In this article, we determine all finite groups such that the minimum degree and the vertex connectivity of PE(G) are equal. Also, we classify all groups whose (proper) enhanced power graphs are strongly regular. Further, the vertex connectivity of the enhanced power graphs associated to some nilpotent groups is obtained. Finally, we obtain a lower bound and an upper bound for the Wiener index of PE(G), where G is a nilpotent group. The finite nilpotent groups attaining these bounds are also characterized.