On the Aα-Spectrum of Superpower Graphs Associatedwith Dihedral Groups

Mir, Basit Auyoob; Atik, Fouzul; Rather, Bilal Ahmad

doi:10.22049/cco.2026.30978.2688

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	On the Aα-Spectrum of Superpower Graphs Associatedwith Dihedral Groups
Communications in Combinatorics and Optimization
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 خرداد 1405 اصل مقاله (607.65 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2026.30978.2688
نویسندگان
Basit Auyoob Mir¹؛ Fouzul Atik¹؛ Bilal Ahmad Rather^* ²
¹Department of Mathematics, SRM University-AP, Andhra Pradesh 522240, India
²Department of Mathematics, Samarkand International University of Technology, Samarkand 140100, Uzbekistan
چکیده
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.
کلیدواژه‌ها
$A_\alpha$-adjacency matrix؛ Laplacian Matrix؛ Eigenvalues؛ Power Graph؛ Dihedral group

مراجع
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On the Aα-Spectrum of Superpower Graphs Associatedwith Dihedral Groups