Matching in power graphs of finite groups

2021/07/02 by Peter J‎. Cameron, Cameron, Peter J., V V Swathi +3
Computer Science · Mathematics · #05C25 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications

paper · doi:10.48550/arxiv.2107.01157

openalex publication_date 2021/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The power graph P(G) of a finite group G is the undirected simple graph with vertex set G, where two elements are adjacent if one is a power of the other. In this paper, the matching numbers of power graphs of finite groups are investigated. We give upper and lower bounds, and conditions for the power graph of a group to possess a perfect matching. We give a formula for the matching number for any finite nilpotent group. In addition, using some elementary number theory, we show that the matching number of the enhanced power graph P_e(G) of G (in which two elements are adjacent if both are powers of a common element) is equal to that of the power graph of G.

Related

• Some results in a new power graphs in finite groups
• k-Power Graphs of Finite Groups
• On the enhanced power graph of a group
• Finite groups with the same Power graph
• Characterizing finite nilpotent groups associated with a graph theoretic\n equality