Eigenvalue-Free Interval for Seidel Matrices of Cographs

Abstract:

      The distribution of Seidel eigenvalues of cographs is investigated in this paper. We prove that there is no Seidel eigenvalue of nontrivial cographs in the interval $(-1, 1)$. We also show the optimality of the interval $(-1,1)$ in the sense that for any $\epsilon>0$ either of the intervals $(1,1+\epsilon)$ and $(-1-\epsilon,-1)$ contains a Seidel eigenvalue of some cograph of order $n$ when $n$ is sufficiently large.