On the Aα-Spectrum of Superpower Graphs Associatedwith Dihedral Groups

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, SRM University-AP, Andhra Pradesh 522240, India

2 Department of Mathematics, Samarkand International University of Technology, Samarkand 140100, Uzbekistan

Abstract

The superpower graph $\mathcal{S}_\Gamma$ of a finite group $\Gamma$ is an undirected simple graph whose vertices are the elements of the group $\Gamma$, and two distinct vertices $a,b\in \Gamma$ 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 investigate the $A_\alpha$-adjacency spectral properties of the superpower graph of groups $D_p\times D_p, D_{p^{k}}, D_{pqr}$, and $D_{p^2q}$, where $p,q,r$ are primes. In particular, we obtain the adjacency, the Laplacian and the signless Laplacian spectra of these graphs, and thereby we prove that the superpower graphs of $D_p\times D_p, $ and $ D_{p^{k}},$ are Laplacain integral.

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References

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Communications in Combinatorics and Optimization

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Available Online from 07 June 2026

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