If the edges of a bipartite graph are such that they can be seen as a disjoint union of perfect matchings then will this somehow reflect in the eigenvalues of the Laplacian?

It would be helpful to get any references which connect the concept of perfect matchings and graph eigenvalues...

Can something be said if the edges of the above bipartite graph decompose as a disjoint union of say $k$ perfect matchings and a part of another?