PIMS Voyageur Colloquium

  • Date: 02/04/2011
Qing Xiang, University of Delaware

University of Calgary


Large cyclotomic strongly regular graphs and nonamorphic fusion schemes of the cyclotomic schemes.




A strongly regular graph srg(v,k,lambda,mu) is a graph with v
vertices that is regular of valency k and that has the following


(1) For any two adjacent vertices x,y, there are exactly lambda
vertices adjacent to both x and y.


(2) For any two nonadjacent vertices x,y, there are exactly mu
vertices adjacent to both x and y.


Classical examples of strongly regular graphs include the Paley


Let q=4t+1 be a prime power. The Paley graph P(q) is the graph with
the finite field F_q as vertex set, where two vertices are adjacent when
they differ by a (nonzero) square. The Paley graphs are the simplest
examples of the so-called cyclotomic strongly regular graphs. In this
talk we will consider cyclotomic srgs Cay(F_q, D) in a broader sense,
namely, D is a union of cosets of a subgroup of the multiplicative group


F_q^* of F_q , not just a single coset of a subgroup of F_q^*. Twelve
new infinite families of srgs are obtained this way. We also show that
these srgs give rise to some very interesting association schemes. This
is a joint work with Tao Feng.


Contact the speaker organizer:


ccunning@ucalgary.ca (PIMS
Calgary site director)