The row left rank of a quaternion unit gain graph in terms of maximum degree
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917981420781568 |
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| author | Lu, Yong Shen, Qi |
| author_facet | Lu, Yong Shen, Qi |
| contents | Let $Φ=(G,U(\mathbb{Q}),φ)$ be a quaternion unit gain graph (or $U(\mathbb{Q})$-gain graph) of order $n$, $A(Φ)$ be the adjacency matrix of $Φ$ and $r(Φ)$ be the row left rank of $Φ$. Let $Δ$ be the maximum degree of $Φ$. In this paper, we prove that $r(Φ)\geq\frac{n}Δ$. Moreover, if $Φ$ is connected, we obtain that $r(Φ)\geq\frac{n-2}{Δ-1}$. All the corresponding extremal graphs are characterized. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06674 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The row left rank of a quaternion unit gain graph in terms of maximum degree Lu, Yong Shen, Qi Combinatorics Let $Φ=(G,U(\mathbb{Q}),φ)$ be a quaternion unit gain graph (or $U(\mathbb{Q})$-gain graph) of order $n$, $A(Φ)$ be the adjacency matrix of $Φ$ and $r(Φ)$ be the row left rank of $Φ$. Let $Δ$ be the maximum degree of $Φ$. In this paper, we prove that $r(Φ)\geq\frac{n}Δ$. Moreover, if $Φ$ is connected, we obtain that $r(Φ)\geq\frac{n-2}{Δ-1}$. All the corresponding extremal graphs are characterized. |
| title | The row left rank of a quaternion unit gain graph in terms of maximum degree |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2504.06674 |