Spectral characterizations of two families of nearly complete bipartite graphs

Chia-an Liu, Chih-wen Weng

Published 2016-01-26Version 1

It is not hard to find many complete bipartite graphs which are not determined by their spectra. We show that the graph obtained by deleting an edge from a complete bipartite graph is determined by its spectrum. We provide some graphs, each of which is obtained from a complete bipartite graph by adding a vertex and an edge incident on the new vertex and an original vertex, which are not determined by their spectra.