On the strong domination number of proper enhanced power graphs of finite groups

TL;DR

This paper investigates the strong domination number of proper enhanced power graphs in finite nilpotent groups, providing new insights into their structural properties and domination parameters.

Contribution

It determines the strong domination number for proper enhanced power graphs specifically in finite nilpotent groups, a novel focus in graph theory of groups.

Findings

Exact strong domination numbers for certain classes of finite nilpotent groups

Characterization of dominating vertices in enhanced power graphs

Insights into the structure of proper enhanced power graphs

Abstract

The enhanced power graph of a group G is a graph with vertex set G, where two distinct vertices x and y are adjacent if and only if there exists an element w in G such that both x and y are powers of w. To obtain the proper enhanced power graph, we consider the induced subgraph on the set G\D, where D represents the set of dominating vertices in the enhanced power graph. In this paper, we aim to determine the strong domination number of the proper enhanced power graphs of finite nilpotent groups.