Vertex-transitive Neumaier graphs
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908579756244992 |
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| author | Jazaeri, Mojtaba |
| author_facet | Jazaeri, Mojtaba |
| contents | A graph $Γ$ is called edge-regular whenever it is regular and for any two adjacent vertices, the number of their common neighbors is independent of the choice of vertices. A clique $C$ in $Γ$ is called regular whenever for any vertex out of $C$, the number of its neighbors in $C$ is independent of the vertex. A Neumaier graph is a non-complete edge-regular graph with a regular clique. In this paper, we study vertex-transitive Neumaier graphs. We give a necessary and sufficient condition under which a vertex-transitive Neumaier graph is strongly regular. We also identify Neumaier Cayley graphs with small valency at most $10$ among vertex-transitive Neumaier graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13722 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vertex-transitive Neumaier graphs Jazaeri, Mojtaba Combinatorics A graph $Γ$ is called edge-regular whenever it is regular and for any two adjacent vertices, the number of their common neighbors is independent of the choice of vertices. A clique $C$ in $Γ$ is called regular whenever for any vertex out of $C$, the number of its neighbors in $C$ is independent of the vertex. A Neumaier graph is a non-complete edge-regular graph with a regular clique. In this paper, we study vertex-transitive Neumaier graphs. We give a necessary and sufficient condition under which a vertex-transitive Neumaier graph is strongly regular. We also identify Neumaier Cayley graphs with small valency at most $10$ among vertex-transitive Neumaier graphs. |
| title | Vertex-transitive Neumaier graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.13722 |