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arXiv · 1809.10029

There does not exist a distance-regular graph with intersection array $\{80, 54,12; 1, 6, 60\}$

Jack H. Koolen·Quaid Iqbal·Jongyook Park·Masood Ur Rehman
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Abstract

In this paper we will show that there does not exist a distance-regular graph $\Gamma$ with intersection array $\{80, 54,12; 1, 6, 60\}$. We first show that a local graph $\Delta$ of $\Gamma$ does not contain a coclique with 5 vertices, and then we prove that the graph $\Gamma$ is geometric by showing that $\Delta$ consists of 4 disjoint cliques with 20 vertices. Then we apply a result of Koolen and Bang to the graph $\Gamma$, and we could obtain that there is no such a distance-regular graph.

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Jack H. Koolen, Quaid Iqbal, Jongyook Park, Masood Ur Rehman. 2018-09-26. There does not exist a distance-regular graph with intersection array $\{80, 54,12; 1, 6, 60\}$. https://arxiv.org/abs/1809.10029

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