Various spectra and energies of subgroup generating bipartite graph
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| Format: | Preprint |
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2026
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| _version_ | 1866917188481318912 |
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| author | Das, Shrabani Erfanian, Ahmad Nath, Rajat Kanti |
| author_facet | Das, Shrabani Erfanian, Ahmad Nath, Rajat Kanti |
| contents | Let $L(G)$ be the set of all subgroups of a group $G$. The subgroup generating bipartite graph $\mathcal{B}(G)$ defined on $G$ is a bipartite graph whose vertex set is partitioned into two sets $G \times G$ and $L(G)$, and two vertices $(a, b) \in G \times G$ and $H \in L(G)$ are adjacent if $H$ is generated by $a$ and $b$. In this paper, we compute various spectra and energies of $\mathcal{B}(G)$ and determine whether $\mathcal{B}(G)$ is hypoenergetic, hyperenergetic, CN-hyperenergetic, L-hyperenergetic or Q-hyperenergetic if $G$ is a dihedral group of order $2p$ and $2p^2$ and dicyclic group of order $4p$ and $4p^2$, where $p$ is any prime. We also show that $\mathcal{B}(G)$ satisfies E-LE conjecture for these groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_04004 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Various spectra and energies of subgroup generating bipartite graph Das, Shrabani Erfanian, Ahmad Nath, Rajat Kanti Group Theory Let $L(G)$ be the set of all subgroups of a group $G$. The subgroup generating bipartite graph $\mathcal{B}(G)$ defined on $G$ is a bipartite graph whose vertex set is partitioned into two sets $G \times G$ and $L(G)$, and two vertices $(a, b) \in G \times G$ and $H \in L(G)$ are adjacent if $H$ is generated by $a$ and $b$. In this paper, we compute various spectra and energies of $\mathcal{B}(G)$ and determine whether $\mathcal{B}(G)$ is hypoenergetic, hyperenergetic, CN-hyperenergetic, L-hyperenergetic or Q-hyperenergetic if $G$ is a dihedral group of order $2p$ and $2p^2$ and dicyclic group of order $4p$ and $4p^2$, where $p$ is any prime. We also show that $\mathcal{B}(G)$ satisfies E-LE conjecture for these groups. |
| title | Various spectra and energies of subgroup generating bipartite graph |
| topic | Group Theory |
| url | https://arxiv.org/abs/2601.04004 |