Weakly cospectral graphs
In the paper finite pseudographs and pseudodigraphs, i.e. undirected and directed finite graphs with multiple edges and loops, are considered. Two pseudographs (pseudodigraphs) \(G\) and \(F\) are called weakly cospectral if each eigenvalue of the adjacency matrix \(M(G)\) of the pseudograph (pseudodigraph) \(G\) is an eigenvalue of the adjacency matrix \(M(F)\) of the pseudograph (pseudodigraph) \(F\) and vice versa. It is proved that any set of finite pairwise nonisomorphic weakly cospectral connected pseudographs, as well as any set of pseudodigraphs satisfying various additional conditions is finite.
scientific article; zbMATH DE number 2121389