Independent spanning trees of product graphs

Abstract

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 G1 is an n1-channel graph and G2 is an n2-channel graph, then G1 × G 2 is an (n1 + n2)-channel graph. We prove this fact by a construction of n1 + n2 independent spanning trees of G1 × G2 from n1 independent spanning trees of G1 and n2 independent spanning trees of G2.