Sesqui-Regular Graphs with Smallest Eigenvalue at Least $-3$

  • Qianqian Yang
  • Brhane Gebremichel
  • Masood Ur Rehman
  • Jae Young Yang
  • Jack H. Koolen
DOI: https://doi.org/10.37236/12174

Abstract

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 $c \geq9$ and valency $k$ is sufficiently large, are $1$-integrable, and as a consequence we classify them.

Published
2026-08-07
How to Cite
Yang, Q., Gebremichel, B., Ur Rehman, M., Yang, J.-Y., & Koolen, J. (2026). Sesqui-Regular Graphs with Smallest Eigenvalue at Least $-3$. The Electronic Journal of Combinatorics, 33(3), #P3.20. https://doi.org/10.37236/12174
Issue
Volume 33, Issue 3 (2026)
Article Number
P3.20