On Graphs Whose Second Largest Eigenvalue Is Less Than 1
第二大根小于1的简单图

Let $G$ be a simple graph with $n$ vertices, and let$\lambda_1(G)\geq\lambda_2(G)\geq\cdots\geq\lambda_n(G)$ be the eigenvalues of theadjacency matrix of $G$. We call $\lambda_2(G)$ the second largest eigenvalue of $G$.In this paper, all the non-bipartite graphs with girth $g\geq4$ and all thebipartite graphswhose second largest eigenvalue is less than 1 have been determined.