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.
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Makhnev, A.A., Paduchikh, D.V. On Automorphisms of Distance-Regular Graph with Intersection Array \(\{18,15,9;\,1,1,10\}\) . Commun. Math. Stat. 3, 527–534 (2015). https://doi.org/10.1007/s40304-015-0072-z
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DOI: https://doi.org/10.1007/s40304-015-0072-z