Sydney University Algebra Seminar

    University of Sydney

    School of Mathematics and Statistics

    Algebra Seminar

    Paul Hafner
    University of Auckland

    On the Hoffman-Singleton graph and related graphs

    Friday 6th September, 12-1pm, Carslaw 373.

    The Hoffman-Singleton graph is the unique Moore graph of order 50, degree 7, diameter 2 and girth 5. In 1998, three infinite families of graphs, modelled on the Hoffman-Singleton graph, were constructed by McKay, Miller and Siran, using voltage assignments.

    In the course of studying these graphs it emerged that Robertson's pentagon-pentagram construction of the Hoffman-Singleton graph should be seen as describing the incidence graph of a bi-affine plane with some additional edges. The `same' description applies to the graphs of McKay-Miller-Siran and is instrumental in the determination of their automorphism groups.

    We will describe these developments, concentrating on the example of the Hoffman-Singleton graph. We will also look at the geometric interpretation of 15-cocliques in the Hoffman-Singleton graph which are important in the construction of the Higman-Sims graph.