Optimal Independent Spanning Trees on Cartesian Product of Hybrid Graphs

A set of k spanning trees rooted at the same vertex r in a graph G are called independent spanning trees (ISTs) if for any vertex x 6= r, the k paths from v to r, one path in each tree, are internally disjoint. The design of ISTs on graphs has applications to fault-tolerant broadcasting and secure message distribution in networks. It was conjectured that for any k-connected graph there exist k ISTs rooted at any vertex of the graph. The conjecture has been proved true for k-connected graphs with k 6 4, and remains open otherwise. In this paper, we deal with the problem of constructing ISTs on Cartesian product of a sequence of hybrid graphs including cycles and complete graphs. Consequently, this result generalizes a number of previous works. Keyword: independent spanning trees; Cartesian product; fault-tolerant broadcasting;