ОБ АВТОМОРФИЗМАХ ДИСТАНЦИОННО РЕГУЛЯРНОГО ГРАФА С МАССИВОМ ПЕРЕСЕЧЕНИЙ {69,56,10;1,14,60}

Translated title of the contribution: On automorphisms of a distance-regular graph with intersection array {69,56,10;1,14,60}

Александр Алексеевич Махнев, Марина Сефовна Нирова

Research output: Contribution to journalArticlepeer-review

Abstract

Let be a distance-regular graph of diameter 3 with eigenvalues . If , then the graph is strongly regular and the complementary graph is pseudogeometric for . If does not contain triangles and the number of its vertices~ is less than 800, then has intersection array {69,56,10;1,14,60}. In this case is a graph with parameters (392,46,0,6) and is a strongly regular graph with parameters (392,115,18,40). Note that the neighborhood of any vertex in a graph with parameters (392,115,18,40) is a strongly regular graph with parameters (115,18,1,3), and its existence is unknown. In this paper, we find possible automorphisms of this strongly regular graph and automorphisms of a distance-regular graph with intersection array {69,56,10;1,14,60}. In particular, it is proved that the latter graph is not arc-transitive.
Translated title of the contributionOn automorphisms of a distance-regular graph with intersection array {69,56,10;1,14,60}
Original languageRussian
Pages (from-to)182-190
Number of pages9
JournalТруды института математики и механики УрО РАН
Volume23
Issue number3
DOIs
Publication statusPublished - 2017

GRNTI

  • 27.45.00

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  • VAK List

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