University of Sydney

Algebra Seminar

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### Commuting involution graphs

Friday 14th, March 12:05-12:55pm, Stephen Roberts.

For a group G, and X a subset of G, let \mathcal C(G,X) denote the graph whose vertex set is X with two (distinct) vertices x and y joined by an edge whenever they are commuting elements of G. If X just consists of involutions we call C(G,X) a commuting involution graph. In this lecture we shall further assume that X is a G conjugacy class. We discuss recent results for various choices of G and X, including the case where G\cong Sym(n), the symmetric group of degree n.