On some characterizations of strong power graphs of finite groups

2015/04/23 by A. K. Bhuniya, Bhuniya, A. K., Sudip Bera +1
Computer Science · Mathematics · #05C25 #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Interconnection Networks and Systems

paper · pdf · doi:10.48550/arxiv.1504.06095

openalex publication_date 2015/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group of order n. The strong power graph P_s(G) of G is the undirected graph whose vertices are the elements of G such that two distinct vertices a and b are adjacent if a^m₁=b^m₂ for some positive integers m₁ ,m₂ < n. In this article we classify all groups G for which P_s(G) is line graph and Caley graph. Spectrum and permanent of the Laplacian matrix of the strong power graph P_s(G) are found for any finite group G.

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