On the integrability of strongly regular graphs

TL;DR

This paper investigates the conditions under which strongly regular graphs with certain spectral properties are 2-integrable, establishing a new lower bound for their minimal valency.

Contribution

It proves that the minimal valency for such graphs must be at least 166, refining previous bounds and advancing understanding of their integrability.

Findings

Lower bound for minimal valency is 166.

Connected graphs with eigenvalue ≥ -3 and high valency are 2-integrable.

Provides new insights into the spectral properties of strongly regular graphs.

Abstract

Koolen et al. showed that if a connected graph with smallest eigenvalue at least $-3$ has large minimal valency, then it is $2$-integrable. In this paper, we will prove that a lower bound for the minimal valency is 166.