Maximal Canonical Graphs with Three Negative Eigenvalues


Aleksandar Torgašev


A connected graph $G$ is called canonical if no two of its nonadjacent vertices have the same neighbours in $G$. Let $C(3)$ be the class of all nonisomorphic canonical graphs with exactly 3 negative eigenvalues (including also their multiplicities). In this paper we prove that the class $C(3)$ contains exactly 32 maximal graphs with respect to relation to be induced subgraph. The orders of these graphs run over the set $\{9, 10, 11, 12, 13, 14\}$.