Assignment 3 François Séguin

Question 1 First, we have that λ − λ − 2 = (λ + 1)(λ − 2). Therefore, it is true that the eigenvalues of the corresponding adjacency matrix come in pairs of additive inverse. However, notice that ± √ −1 are eigenvalues, and therefore the associated matrix cannot be symmetric (there would only be real eigenvalues). We conclude that no undirected graph can have the above characteristic polynomial, let alone a bipartite graph.