Line Graph Characterization of Cyclic Subgroup Graph
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866929761595424768 |
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| author | Malviy, Siddharth Kakkar, Vipul Srivastava, Swapnil |
| author_facet | Malviy, Siddharth Kakkar, Vipul Srivastava, Swapnil |
| contents | The cyclic subgroup graph ${Γ(G)}$ of a group $G$ is the simple undirected graph with cyclic subgroups as a vertex set and two distinct vertices $H_1$ and $H_2$ are adjacent if and only if $H_1 \leq H_2$ and there does not exist any cyclic subgroup $K$ such that $H_1 < K < H_2$. In this paper, we classify all the finite groups $G$ such that $Γ(G)$ is the line graph of some graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12184 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Line Graph Characterization of Cyclic Subgroup Graph Malviy, Siddharth Kakkar, Vipul Srivastava, Swapnil Combinatorics The cyclic subgroup graph ${Γ(G)}$ of a group $G$ is the simple undirected graph with cyclic subgroups as a vertex set and two distinct vertices $H_1$ and $H_2$ are adjacent if and only if $H_1 \leq H_2$ and there does not exist any cyclic subgroup $K$ such that $H_1 < K < H_2$. In this paper, we classify all the finite groups $G$ such that $Γ(G)$ is the line graph of some graph. |
| title | Line Graph Characterization of Cyclic Subgroup Graph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.12184 |