Subgraphs and the Laplacian spectrum of a graph

Let G be a graph and H a subgraph of G. In this paper, a set of pairwise independent subgraphs that are all isomorphic copies of H is called an H-matching. Denoting by ν(H,G) the cardinality of a maximum H-matching in G, we investigate some relations between ν(H,G) and the Laplacian spectrum of G.