SUPERPOWER GRAPHS OF FINITE ABELIAN GROUPS

Abstract

For a finite group G, the superpower graph S(G) is a simple undirected graph with vertex set G, where two distinct vertices are adjacent if and only if the order of one divides that of the other. The aim of this paper is to provide tight bounds for the vertex connectivity of S(G), together with some structural properties such as maximal domination sets, Hamiltonicity, and its variations for superpower graphs of finite abelian groups. The paper concludes with some open problems. © (2024), (Union Matematica Argentina). All Rights Reserved.