Classifies sesqui-regular graphs as 1-integrable with eigenvalue -3 and high valency, suggesting new structural insights.
Koolen Yang and Yang showed that if a graph with smallest eigenvalue at least $-3$ has large minimal valency, then it is $2$-integrable. In this paper, we show that sesqui-regular graphs with smallest eigenvalue at least $-3$ and parameters $(n,k,c)$, where c ≥9 and valency k is sufficiently large, are $1$-integrable, and as a consequence we classify them.
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Yang et al. (2026) studied this question.
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