On the resistance regular graphs
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912425971810304 |
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| author | T, Haritha A V, Chithra |
| author_facet | T, Haritha A V, Chithra |
| contents | For a connected graph $G$, its resistance distance matrix is denoted by $R(G)$. A graph is called resistance regular if all the row (or column) sums of $R(G)$ are equal. We provide a necessary and sufficient condition for a simple connected graph to be resistance regular. Additionally, we establish sharp bounds for the resistance spectral radius and present various bounds for the resistance energy of $G$. Furthermore, we compute the resistance spectrum and resistance energy of some resistance regular graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the resistance regular graphs T, Haritha A V, Chithra Combinatorics 05C50, 05C76 For a connected graph $G$, its resistance distance matrix is denoted by $R(G)$. A graph is called resistance regular if all the row (or column) sums of $R(G)$ are equal. We provide a necessary and sufficient condition for a simple connected graph to be resistance regular. Additionally, we establish sharp bounds for the resistance spectral radius and present various bounds for the resistance energy of $G$. Furthermore, we compute the resistance spectrum and resistance energy of some resistance regular graphs. |
| title | On the resistance regular graphs |
| topic | Combinatorics 05C50, 05C76 |
| url | https://arxiv.org/abs/2405.18177 |