On Graphs in Which Neighborhoods of Vertices Are Strongly Regular with Parameters (85,14,3,2) or (325,54,3,10)

被引：0
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作者：
M. M. Isakova
A. A. Makhnev
A. A. Tokbaeva
机构：
[1] Kabardino-Balkarian State University,Krasovskii Institute of Mathematics and Mechanics
[2] Ural Branch of the Russian Academy of Sciences,undefined
[3] Ural Federal University,undefined
来源：
Proceedings of the Steklov Institute of Mathematics | 2017年 / 299卷
关键词：
strongly regular graph; locally ; -graph; automorphism of a graph.;
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摘要：
J. Koolen posed the problem of studying distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with nonprincipal eigenvalue at most t for a given positive integer t. This problem was solved earlier for t = 3. In the case t = 4, the problem was reduced to studying graphs in which neighborhoods of vertices have parameters (352,26,0,2), (352,36,0,4), (243,22,1,2), (729,112,1,20), (204,28,2,4), (232,33,2,5), (676,108,2,20), (85,14,3,2), or (325,54,3,10). In the present paper, we prove that a distance-regular graph in which neighborhoods of vertices are strongly regular with parameters (85, 14, 3, 2) or (325, 54, 3, 10) has intersection array {85, 70, 1; 1, 14, 85} or {325, 270, 1; 1, 54, 325}. In addition, we find possible automorphisms of a graph with intersection array {85, 70, 1; 1, 14, 85}.
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页码：68 / 74
页数：6
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