We investigate strongly regular graphs for which Hoffman's ratio bound and Cvetcović's inertia bound are equal. This means that ve−=m−(e−−k), where v is the number of vertices, k is the regularity, e− is the smallest eigenvalue, and m− is the multiplicity of e−. We show that Delsarte cocliques do not exist for all Taylor's 2‐graphs and for point graphs of generalized quadrangles of order (q,q2−q) for infinitely many q. For cases where equality may hold, we show that for nearly all parameter sets, there are at most two Delsarte cocliques.
Journal of Combinatorial Designs – Wiley
Published: Jan 1, 2018
Keywords: ; ; ; ; ; ; ; ;
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