Graphs With All But Two Eigenvalues In [−2, 0]

Abstract

The eigenvalues of a graph are those of its adjacency matrix. Recently, Cioabă, Haemers and Vermette characterized all graphs with all but two eigenvalues equal to −2 and 0. In this article, we extend their result by characterizing explicitly all graphs with all but two eigenvalues in the interval [−2, 0]. Also, we determine among them those that are determined by their spectrum.

Keywords

• graph spectrum
• complete multipartite graph
• graph determined by its spectrum
• 05c50