Dale Mesner, Higman & Sims, and the strongly regular graph (1100, 22, 0, 6)
natisniAndrew Woldar (Villanova University, USA)
It is not widely known that the SRG $\Gamma$ in our title, commonly referred to as the Higman-Sims graph, was actually discovered by Dale Mesner in 1956, and its uniqueness established by Mesner in 1964. In Mesner's terminology, $\Gamma$ was one of a putative family of graphs of Negative Latin Square type having no triangles.
Our focus in this talk will be equally distributed between psychology and history of these independent discoveries by Mesner and Higman \& Sims, together with a discussion of some significant properties of $\Gamma$. In particular, Mesner's construction will be considered in modern clothing.
Our talk will be arranged to supplement the plenary lecture of coauthor MK, in particular showcasing $\Gamma$
as a universal object for all known primitive SRGs with no triangles.
Joint work with Mikhail Klin.
