By Jagdish Srivastava

ISBN-10: 0720422620

ISBN-13: 9780720422627

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And J. H. VAN LINT and J. J. SEIDEL Technological University of Eindhoven, Eindhoven, The Netherlands By use of the perfect ternary Golay code, a strongly regular graph on 243 vertices is constructed, having the property that any adjacent pair of vertices is in one tri­ angle and that any nonadjacent pair of vertices is in one quadrangle. The graph realizes one of the five possibilities for graphs with this property. It provides a (243, 22, 2)-system on 22 and 23 in the sense of Bridges and Ryser [1969].

Denote by a(G) the stability number of G (maximum cardinality of a stable set), by 6(G) the partition number of G (smallest number of cliques which cover X), by y(G) the chromatic number of G, and by a>{G) the density number of G (maximum number of elements in a clique). The three following statements are equivalent: (1) OL(GA,D) = 9(GA,D) for every A and every D. (2) y(GA,D) = CO(GA,D) for every A and every D. (3) every odd cycle in G contains at least one edge with the property that every maximal clique containing this edge contains a third vertex of the cycle.

1. Introduction Combinatorial mathematics or combinatorial theory concerns itself with the problems of operations on or arrangements and selections from a finite or discrete set. Though mathematicians have concerned themselves with specific combinatorial problems since ancient times, the emergence of combinatorial mathematics as a distinct discipline is of comparatively recent date. Many classical results of combinatorial mathematics were obtained in connection with the development of probability theory since the times of Pascal and Fermat.

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A Survey of Combinatorial Theory by Jagdish Srivastava


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