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The integrability of sesqui-regular graphs with smallest eigenvalue at least $-3$
In this paper, we prove that every connected sesqui-regular graph with parameters $(n,k,c)$, where $c\geq3$, and with smallest eigenvalue in $[-3,-2)$ is $1$-integrable if its valency is sufficiently large. The bound on $c$ is optimal: for every integer $t\geq2$, the Cartesian product of the Shrikha
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