k-Power Graphs of Finite Groups
Swathi V V, M S Sunitha

TL;DR
This paper explores the properties of k-power graphs of finite groups, analyzing their structure and parameters, with specific focus on cyclic groups and an application of these graphs.
Contribution
It introduces the concept of k-power graphs for finite groups, investigates their graph parameters, and examines properties of cyclic groups' k-power graphs, including an application.
Findings
Determined the number of edges and clique number of k-power graphs.
Analyzed connectedness properties of k-power graphs.
Identified specific properties for cyclic groups' k-power graphs.
Abstract
For a finite group and for a fixed positive integer , , the -power graph of is an undirected simple graph with vertex set in which two distinct vertices and are adjacent if and only if or . In this paper, we investigate some graph parameters such as number of edges, clique number, connectedness, etc. of -power graphs of finite groups. Also find some properties of -power graphs of finite cyclic groups, and finally we present an application
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Graph Labeling and Dimension Problems
