On the distribution of eigenvalues of a simple undirected graph Original Research Article

For a simple, undirected graph Gn, let λi(Gn) be the ith largest eigenvalue of Gn. This paper presents mainly the following: 1. For ngreater-or-equal, slanted4, if Gn is incomplete, thenimage 2. Seven sufficient and necessary conditions such that λ2(Gn)=−1. 3. λ3(Gn)=−1 implies that λj(Gn)=−1, j=3,4,…,n−1.