Codes and Expansions (CodEx) Seminar

Krystal Guo (University of Amsterdam and QuSoft):
Strongly regular graphs with a regular point

Arising from Hoffman and Singleton's study of Moore graphs, strongly regular graphs play an important role in algebraic graph theory. Strongly regular graphs can be constructed from various geometric objects, such as finite geometries and generalized quadrangles. Certain geometric properties, such as having a regular point, can be studied in the context of graphs, using combinatorial and algebraic tools. We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the structure of such graphs, we characterize all graphs containing such a vertex, thereby, answering a question posed by Gardiner, Godsil, Hensel, and Royle. As a by-product of our characterisation, we are able to give new constructions of infinite families of strongly regular graphs and compute many small sporadic examples; for example, we find 135478 new strongly regular graphs with parameters (85,20,3,5). This is joint work with Edwin van Dam.