Sombor Spectrum of Super Graphs defined on groups

Given a simple graph $A$ on a group $G$ and an equivalence relation $B$ on $G$, the $B$ super $A$ graph is defined as a simple graph, whose vertex set is $G$ and two vertices $g$, $h$ are adjacent if either they are in the same equivalence class or there exist $g^{\prime} \in[g]$ and $h^{\prime} \in[h]$ such that $g^{\prime}$ and $h^{\prime}$ are adjacent in $A$. In the literature, the $B$ super $A$ graphs have been investigated by considering $A$ to be either power graph, enhanced power graph, or commuting graph and $B$ to be an equality, order or conjugacy relation. In this paper, we investigate the Sombor spectrums of these $B$ super $A$ graphs for certain non-abelian groups, viz. the dihedral group, generalized quaternion group and the semidihedral group, respectively.

Publication Details

Journal
ArXiv.org
Published
2025-04-21
Primary Topic
Graph theory and applications
Type
article
Field-Weighted Citation Impact
0.00

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article

Sombor Spectrum of Super Graphs defined on groups

ArXiv.org
Graph theory and applications
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Sombor Spectrum of Super Graphs defined on groups

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Abstract

Given a simple graph $A$ on a group $G$ and an equivalence relation $B$ on $G$, the $B$ super $A$ graph is defined as a simple graph, whose vertex set is $G$ and two vertices $g$, $h$ are adjacent if either they are in the same equivalence class or there exist $g^{\prime} \in[g]$ and $h^{\prime} \in[h]$ such that $g^{\prime}$ and $h^{\prime}$ are adjacent in $A$. In the literature, the $B$ super $A$ graphs have been investigated by considering $A$ to be either power graph, enhanced power graph, or commuting graph and $B$ to be an equality, order or conjugacy relation. In this paper, we investigate the Sombor spectrums of these $B$ super $A$ graphs for certain non-abelian groups, viz. the dihedral group, generalized quaternion group and the semidihedral group, respectively.

ArXiv.org
Arthritis National Research Foundation, Science and Engineering Research Board
Openalex Percentile: Top 44%
Graph theory and applications
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Sombor Spectrum of Super Graphs defined on groups · ArXiv.org (2025) | TGRS Research Map | TGRS