On the independent spanning trees of recursive circulant graphs G(cdm,d) with d>2

Two spanning trees of a graph G are said to be independent if they are rooted at the same vertex r, and for each vertex v≠r in G, the two different paths from v to r, one path in each tree, are internally disjoint. A set of spanning trees of G is independent if they are pairwise independent. The construction of multiple independent spanning trees has many applications in network communication. For instance, it is useful for fault-tolerant broadcasting and secure message distribution. A recursive circulant graph G(N,d) has N=cdm vertices labeled from 0 to N−1, where d⩾2, m⩾1, and 1⩽c2, where the number of independent spanning trees matches the connectivity of G(cdm,d).