Advances in Mathematical Physics (Jan 2020)
Characterization of Graphs with an Eigenvalue of Large Multiplicity
Abstract
Let G be a simple and undirected graph. The eigenvalues of the adjacency matrix of G are called the eigenvalues of G. In this paper, we characterize all the n-vertex graphs with some eigenvalue of multiplicity n−2 and n−3, respectively. Moreover, as an application of the main result, we present a family of nonregular graphs with four distinct eigenvalues.