Bounds for regular induced subgraphs of strongly regular graphs

Abstract

Given feasible strongly regular graph parameters (v, k, λ, µ) and a nonnegative integer d, we determine upper and lower bounds on the order of a d-regular induced subgraph of any strongly regular graph with parameters (v, k, λ, µ). Our new bounds are at least as good as the bounds on the order of a d-regular induced subgraph of a k-regular graph determined by Haemers. Further, we prove that for each non-negative integer d, our new upper bound improves on Haemers' upper bound for infinitely many strongly regular graphs.