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2017•Journal of Siberian Federal University Mathematics & PhysicsOpen access

Automorphisms of the AT4(6; 6; 3)-graph and its Strongly-regular Graphs

Константин С. Ефимов, А. А. Махнев

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Abstract

Koolen and Jurisich defined class of AT 4-graphs (tight antipodal graph of diameter 4).Among these graphs available graph with intersection array {288, 245, 48, 1; 1, 24, 245, 288} on v = 1 + 288 + 2940 + 576 + 2 = 3807 vertices.Antipodal quotient of this graph is strongly regular graph with parameters (1269, 288, 42, 72).Both these graphs are locally pseudo GQ(7, 5)-graphs.In this paper we find possible automorphisms of these graphs.In particular, group of automorphisms of distance-regular graph with intersection array {288, 245, 48, 1; 1, 24, 245, 288} acts intransitive on the set of its antipodal classes.

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Koolen and Jurisich defined class of AT 4-graphs (tight antipodal graph of diameter 4).Among these graphs available graph with intersection array {288, 245, 48, 1; 1, 24, 245, 288} on v = 1 + 288 + 2940 + 576 + 2 = 3807 vertices.Antipodal quotient of this graph is strongly regular graph with parameters (1269, 288, 42, 72).Both these graphs are locally pseudo GQ(7, 5)-graphs.In this paper we find possible automorphisms of these graphs.In particular, group of automorphisms of distance-regular graph with intersection array {288, 245, 48, 1; 1, 24, 245, 288} acts intransitive on the set of its antipodal classes.

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Available abstract

Koolen and Jurisich defined class of AT 4-graphs (tight antipodal graph of diameter 4).Among these graphs available graph with intersection array {288, 245, 48, 1; 1, 24, 245, 288} on v = 1 + 288 + 2940 + 576 + 2 = 3807 vertices.Antipodal quotient of this graph is strongly regular graph with parameters (1269, 288, 42, 72).Both these graphs are locally pseudo GQ(7, 5)-graphs.In this paper we find possible automorphisms of these graphs.In particular, group of automorphisms of distance-regular graph with intersection array {288, 245, 48, 1; 1, 24, 245, 288} acts intransitive on the set of its antipodal classes.

Key concepts: Automorphism, Mathematics, Graph, Combinatorics

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