University of Birmingham > Talks@bham > Algebra Seminar > Primitive triangle free strongly regular graphs, a survey: from Dale Mesner to recent results

Primitive triangle free strongly regular graphs, a survey: from Dale Mesner to recent results

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If you have a question about this talk, please contact David Craven.

In this survey lecture we will try to cover a few topics. First we wish to recall an intriguing hidden history about the unique strongly regular graph NL2(10) with the parameters (100, 22, 0, 6), specifically as it relates to the work of Dale Mesner during the years 1956-1964. We will mention the later independent construction of this graph by D.G. Higman and C.C. Sims, which led them to discover a new sporadic simple group.

We also will discuss in some detail our own computer aided efforts to better understand the graph NL2(10). In fact, this graph contains all known 7 primitive triangle-free strongly graphs (those on 5,10,16,50,56,77 and 100 vertices).

New models for some of these graphs will be presented, which rely on knowledge of a relatively small subgroup of a graph in consideration.

We will finish with a brief discussion of recent attempts and ongoing perspectives in search for new primitive triangle free strongly regular graphs.

This is a joint project together with Matan Ziv-Av (BGU) and Andy Woldar (Villanova, USA ).

This talk is part of the Algebra Seminar series.

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