The Hoffman number of a graph

For a connected graph G with n vertices, let {λ1,λ2,…,λr} be the set of distinct positive eigenvalues of the Laplacian matrix of G. The Hoffman number μ(G) of G is defined by μ(G)=λ1λ2…λr/n. In this paper, we study some properties and applications of the Hoffman number.