An improved bound for strongly regular graphs with smallest eigenvalue $-m$

TL;DR

This paper improves a classical bound on the parameters of primitive strongly regular graphs with a given smallest eigenvalue, and also offers an alternative derivation of a theorem related to orthogonal arrays.

Contribution

The authors provide a tighter bound on bb in terms of m and bc for strongly regular graphs, extending Neumaier's 1979 result, and demonstrate how their methods apply to orthogonal array theory.

Findings

Enhanced bound for bb in strongly regular graphs

Methodology applicable to orthogonal array derivations

Extension of Neumaier's classical result

Abstract

In 1979, Neumaier gave a bound on $\lambda$ in terms of $m$ and $\mu$, where $-m$ is the smallest eigenvalue of a primitive strongly regular graph, unless the graph in question belongs to one of the two infinite families of strongly regular graphs. We improve this result. We also indicate how our methods can be used to give an alternate derivation of Bruck's Completion Theorem for orthogonal arrays.