A structure theory for regular graphs with fixed smallest eigenvalue

Abstract

In this paper we will give a structure theory for regular graphs with fixed smallest eigenvalue. As a consequence of this theory, we show that a $k$-regular graph with smallest eigenvalue $-\lambda$ has clique number linear in $k$ if $k$ is large with respect to $\lambda$.

arXiv commentarXiv admin note: text overlap with arXiv:2011.11935