On the Clique Number of a Strongly Regular Graph

Abstract

We determine new upper bounds for the clique numbers of strongly regular graphs in terms of their parameters. These bounds improve on the Delsarte bound for infinitely many feasible parameter tuples for strongly regular graphs, including infinitely many parameter tuples that correspond to Paley graphs.

On eigenfunctions and maximal cliques of Paley graphs of square order

“…Proof. The lemma immediately follows from Lemmas 7 and 5 (5). Now let us complete the proof of Theorem 1.…”

“…The problem of finding clique (independence) number of Paley graphs is open in general. In [5], the Delsarte bound was improved for infinitely many parameter tuples that correspond to Paley graphs.…”

Upper bounds on the size of transitive subtournaments in digraphs

“…For example, Bachoc, Matolcsi and Ruzsa [1] improved the Delsarte bound for Paley graphs of nonsquare order using the properties of quadratic residues of finite fields. Very recently, it was announced that Greaves and Soicher [4] improved the Delsarte bound for a large class of strongly regular graphs using block-intersection polynomials.…”

“…In particular, we give an analogy of Hoffman's bound for the size of cocliques in a regular graph. Furthermore, we partially improve the Hoffman type bound for doubly regular tournaments by using the technique of Greaves and Soicher for strongly regular graphs [4], which gives a new application of block intersection polynomials.In this paper, we consider analogies of the Hoffman bound and the Greaves-Soicher bound to digraphs. In particular, as an analogy of the Hoffman bound for regular graphs, we show that if a…”

“…In particular, we give an analogy of Hoffman's bound for the size of cocliques in a regular graph. Furthermore, we partially improve the Hoffman type bound for doubly regular tournaments by using the technique of Greaves and Soicher for strongly regular graphs [4], which gives a new application of block intersection polynomials.…”