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1 results

  • 8 - Combinatorial constructions

  • Andries E. Brouwer, Technische Universiteit Eindhoven, The Netherlands, H. Van Maldeghem, Universiteit Gent, Belgium
  • Book:
    Strongly Regular Graphs
    Published online:
    06 January 2022
    Print publication:
    13 January 2022, pp 197-248

  • Summary

    This chapter collects constructions of strongly regular graphs related to some combinatorial setting, where the starting point is not a group. It discusses Hadamard and conference matrices, (mutually orthogonal) Latin squares, symmetric designs, transversal 3-designs, quasi-symmetric designs (including a table of exceptional parameter sets for such designs with up to 100 points, and we review and prove some results ruling out certain parameter sets of those), partial geometries (including a full proof of Bruck’s and Bose’s sufficient conditions for a graph to be the point graph of a partial geometry, and of Neumaier’s ‘claw bound’), semi-partial geometries and partial quadrangles, (regular) two-graphs, pseudo-cyclic association schemes, and spherical designs. We also briefly discuss the t-vertex condition, asymptotic and randomness properties, the chromatic number and index,and directed strongly regular graphs.