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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2411.16734 |
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| _version_ | 1866912132755357696 |
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| author | Kaushik, Varun J Ekta Parveen Kumar, Jitender |
| author_facet | Kaushik, Varun J Ekta Parveen Kumar, Jitender |
| contents | Given a graph $A$ on a group $G$ and an equivalence relation $B$ on $G$, the $B$ super$A$ graph, whose vertex set is $G$ and two vertices $g$, $h$ are adjacent if and only if there exist $g^{\prime} \in[g]$ and $h^{\prime} \in[h]$ such that $g^{\prime}$ and $h^{\prime}$ are adjacent in $A$. Recently, Dalal \emph{et al.} (Spectrum of super commuting graphs of some finite groups, \textit{Computational and Applied Mathematics}, 43(6):348, 2024) obtain the Laplacian spectrum of supercommuting graphs of certain non-abelian groups including the dihedral group and the generalized quaternion group. In this paper, we continue the study of Laplacian spectrum of certian $B$ super$A$ graphs. We obtain the Laplacian spectrum of conjugacy superenhanced power graphs of certain non-abelian groups, namely: dihedral group, generalized quaternion group and semidihedral group. Moreover to enhance the work of Dalal \emph{et al}, we obtain the Laplacian spectrum of conjugacy supercommuting graph of semidihedral group. We prove that graphs considered in this paper are $L$-integral. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16734 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Laplacian Spectrum of Super Graphs defined on Certain Non-abelian Groups Kaushik, Varun J Ekta Parveen Kumar, Jitender Combinatorics Group Theory 05C25, 05C50 Given a graph $A$ on a group $G$ and an equivalence relation $B$ on $G$, the $B$ super$A$ graph, whose vertex set is $G$ and two vertices $g$, $h$ are adjacent if and only if there exist $g^{\prime} \in[g]$ and $h^{\prime} \in[h]$ such that $g^{\prime}$ and $h^{\prime}$ are adjacent in $A$. Recently, Dalal \emph{et al.} (Spectrum of super commuting graphs of some finite groups, \textit{Computational and Applied Mathematics}, 43(6):348, 2024) obtain the Laplacian spectrum of supercommuting graphs of certain non-abelian groups including the dihedral group and the generalized quaternion group. In this paper, we continue the study of Laplacian spectrum of certian $B$ super$A$ graphs. We obtain the Laplacian spectrum of conjugacy superenhanced power graphs of certain non-abelian groups, namely: dihedral group, generalized quaternion group and semidihedral group. Moreover to enhance the work of Dalal \emph{et al}, we obtain the Laplacian spectrum of conjugacy supercommuting graph of semidihedral group. We prove that graphs considered in this paper are $L$-integral. |
| title | Laplacian Spectrum of Super Graphs defined on Certain Non-abelian Groups |
| topic | Combinatorics Group Theory 05C25, 05C50 |
| url | https://arxiv.org/abs/2411.16734 |