Independent spanning trees of product graphs

A graph G is called an n-channel graph at vertex r if there are n independent spanning trees rooted at r. A graph G is called an n-channel graph if for every vertex u, G is an n-channel graph at u. Independent spanning trees of a graph play an important role in fault-tolerant broadcasting in the graph. In this paper we show that if G(1) is an n(1)-channel graph and G(2) is an n(2)-channel graph, then G(1) x G(2) is an (n(1) + n(2))-channel graph. We prove this fact by a construction of n(1) + n(2) independent spanning trees of G(1) x G(2) from n(1) independent spanning trees of G(1) and n(2) independent spanning trees of G(2).