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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.00714 |
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| _version_ | 1866915208564310016 |
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| author | Jazaeri, Mojtaba |
| author_facet | Jazaeri, Mojtaba |
| contents | Let $Γ$ denote a distance-regular graph with diameter $D \geq 2$. Let $E$ denote a primitive idempotent of $Γ$ with respect to which $Γ$ is $Q$-polynomial. Assume that there exists a $3$-clique $\{x,y,z\}$ such that $E\hat{x},E\hat{y},E\hat{z}$ are linearly dependent. In this paper, we classify all the $Q$-polynomial distance-regular graphs $Γ$ with the above property. We describe these graphs from multiple points of view. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $Q$-polynomial distance-regular graphs with a linear dependency involving a $3$-clique Jazaeri, Mojtaba Combinatorics Let $Γ$ denote a distance-regular graph with diameter $D \geq 2$. Let $E$ denote a primitive idempotent of $Γ$ with respect to which $Γ$ is $Q$-polynomial. Assume that there exists a $3$-clique $\{x,y,z\}$ such that $E\hat{x},E\hat{y},E\hat{z}$ are linearly dependent. In this paper, we classify all the $Q$-polynomial distance-regular graphs $Γ$ with the above property. We describe these graphs from multiple points of view. |
| title | On $Q$-polynomial distance-regular graphs with a linear dependency involving a $3$-clique |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.00714 |