On the Difference Graph of power graphs of finite groups
Parveen, Jitender Kumar, Ramesh Prasad Panda

TL;DR
This paper studies the difference graph between the enhanced power graph and the power graph of finite groups, classifying its properties for various group classes and specific groups like symmetric and alternating groups.
Contribution
It characterizes the difference graph's properties for finite groups, especially nilpotent groups, and classifies these graphs for symmetric and alternating groups.
Findings
Difference graphs are chordal, star, and threshold for certain groups.
Nilpotent groups have difference graphs with specific graph class properties.
Classified when difference graphs of symmetric and alternating groups are cograph, bipartite, etc.
Abstract
The power graph of a finite group is a simple undirected graph with vertex set and two vertices are adjacent if one is a power of the other. The enhanced power graph of a finite group is a simple undirected graph whose vertex set is the group and two vertices and are adjacent if there exists such that both and are powers of . In this paper, we investigate the difference graph of a finite group , which is the difference of the enhanced power graph and the power graph of with all isolated vertices removed. We study the difference graphs of finite groups with forbidden subgraphs among other results. We first characterize an arbitrary finite group such that is a chordal graph, star graph, dominatable, threshold graph, and split graph. From this, we conclude that the latter four graph classes are…
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Taxonomy
TopicsSynthesis and properties of polymers · Finite Group Theory Research · graph theory and CDMA systems
