On Automorphisms of Distance-Regular Graph with Intersection Array $\{18,15,9;\,1,1,10\}$

Abstract

Recently, Makhnev and Nirova found intersection arrays of distance-regular graphs with $\lambda =2$ and at most 4096 vertices. In the case of primitive graphs of diameter 3 with $\mu = 1$ there corresponding arrays are $\{18,15,9;1,1,10\}$, $\{33,30,8;1,1,30\}$ or $\{39,36,4;1,1,36\}$. In this work, possible orders and subgraphs of fixed points of the hypothetical distance-regular graph with intersection array $\{18,15,9;1,1,10\}$ are studied. In particular, graph with intersection array $\{18,15,9;1,1,10\}$ is not vertex symmetric.

Keywords

Distance-regular graph / Automorphism / Vertex symmetric graph

References

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Funding

RSF(14-11-00061)