Sesqui-regular graphs with smallest eigenvalue at least $-3$

TL;DR

This paper investigates sesqui-regular graphs with a smallest eigenvalue at least -3, focusing on their integrability properties, extending prior work on graphs with large minimal valency.

Contribution

It specifically analyzes the integrability of sesqui-regular graphs with smallest eigenvalue at least -3, a case not fully explored in previous research.

Findings

Characterization of sesqui-regular graphs with eigenvalue ≥ -3

Conditions under which these graphs are integrable

Extension of previous results on graphs with large minimal valency

Abstract

Koolen et al. showed that if a graph with smallest eigenvalue at least $-3$ has large minimal valency, then it is $2$-integrable. In this paper, we will focus on the sesqui-regular graphs with smallest eigenvalue at least $-3$ and study their integrability.