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

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• Mikhail Klin, Ben-Gurion University of the Negev
• Thursday 16 May 2013, 16:00-17:00
• Watson Building, Lecture Room A.

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.

This talk is included in these lists:

• Algebra seminar
• School of Mathematics events
• Watson Building, Lecture Room A

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