On the Spectral Analysis of the Superpower Graph of the Direct Product of Dihedral Groups

2025/08/09 by Basit Auyoob Mir, Mir, Basit Auyoob, Fouzul Atik +1
Mathematics · #Graph theory and applications #Finite Group Theory Research #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2508.06812

Abstract

The superpower graph of a finite group G, or S_G, is an undirected simple graph whose vertices are the elements of the group G, and two distinct vertices a,b∈ G are adjacent if and only if the order of one vertex divides the order of the other vertex, which means that either o(a)|o(b) or o(b)|o(a). In this paper, we have investigated the A_α-adjacency spectral properties of the superpower graph of the direct product D_p× D_p, where D_p is a dihedral group for p being prime. Also, we have determined its Laplacian and signless Laplacian spectrum by giving different values to α; furthermore, we delved into its superpower graph and deduced the A_α- adjacency spectrum of the superpower graph of D_p× D_p and D_p^m for p being an odd prime.

Citations

• The Order Supergraph of the Power Graph of a Finite Group

Related

• On the Spectral Analysis of Power Graph of Dihedral Groups
• Laplacian Spectrum of Super Graphs defined on Certain Non-abelian Groups
• Universal adjacency spectrum of (proper) power graphs and their complements on some groups
• On the Spectral properties of power graphs over certain groups
• On the power graph of the direct product of two groups