## Lethbridge Number Theory and Combinatorics Seminar: Sara Sasani

- Date: 11/27/2017

University of Lethbridge

A Strongly Regular Decomposition of the Complete Graph and its Association Scheme

A "Strongly Regular Graph", SRG(?,k,lambda,mu), is a k-regular graph with v vertices such that every two adjacent vertices have lambda common neighbors, and every two non-adjacent vertices have mu common neighbors. Let M be any power of 2, and letÂ M' be the square of M.

A construction for M disjoint SRG(M'(M+2),M'+M,M,M) will be shown to form a decomposition of the complete graph with M'(M+2) vertices, if the cliques of size M' is considered as a strongly regular graph with parameter (M'(M+2),M'-1,M'-2,0). By decomposing the cliques and the strongly regular graphs further, we show the existence of a symmetric association scheme with 4M-2 classes and explain, by an example, how to find the first and second eigenmatrices of the scheme.

**Time:** 12:00-12:50pm

**Location:** C630 University Hall