A bound on the girth of quaternion unit gain graphs in terms of the rank
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929608462434304 |
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| author | Khan, Suliman van Dam, Edwin R. |
| author_facet | Khan, Suliman van Dam, Edwin R. |
| contents | We obtain a bound on the girth g of a quaternion unit gain graph in terms of the rank r of its adjacency matrix. In particular, we show that g <= r + 2 and characterize all quaternion unit gain graphs for which g = r+2. This extends corresponding results for (ordinary) graphs, signed graphs, and complex unit gain graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19057 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A bound on the girth of quaternion unit gain graphs in terms of the rank Khan, Suliman van Dam, Edwin R. Combinatorics 05C05, 05C50 We obtain a bound on the girth g of a quaternion unit gain graph in terms of the rank r of its adjacency matrix. In particular, we show that g <= r + 2 and characterize all quaternion unit gain graphs for which g = r+2. This extends corresponding results for (ordinary) graphs, signed graphs, and complex unit gain graphs. |
| title | A bound on the girth of quaternion unit gain graphs in terms of the rank |
| topic | Combinatorics 05C05, 05C50 |
| url | https://arxiv.org/abs/2411.19057 |