A note on cospectral graphs

Abstract

The notion of a (1, x) adjacency matrix is introduced, together with methods for dealing with it. It is shown that in many instances this adjacency matrix is superior to the usual (0, 1) adjacency matrix, and will distinguish cospectral pairs, when the latter will not. In those cases in which the (1, x) adjacency matrix fares no better than the (0, 1) adjacency matrix, a good deal can be said about the matrices by which the cospectral pairs are similar. © 1980.