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Lethbridge Number Theory and Combinatorics Seminar
Date:
November 27, 2017
Time:
12:00-12:50pm
Lecturer(s):
Sara Sasani (U of Lethbridge)
Location:
University of Lethbridge
Topic:
A Strongly Regular Decomposition of the Complete Graph and its Association Scheme
Description (in plain text format):
A "Strongly Regular Graph", SRG(ν,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 let 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.
Other Information:
Location: C630 University Hall
Web page: http://www.cs.uleth.ca/~nathanng/ntcoseminar/
Contact:
Barb Hodgson | hodgsonb@uleth.ca | (403) 329-2470 | uleth.ca/artsci/math-computer-science
