Excessive index for mesh derived networks

A matching in a graph G=(V,E)G=(V,E) is a subset M of edges, no two of which have a vertex in common. A matching M is said to be perfect if every vertex in G is an endpoint of one of the edges in M. The excessive index of a graph G is the minimum number of perfect matchings to cover the edge set of G. In this paper we determine the excessive index for mesh, cylinder and torus networks.