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

Abstract

a b s t r a c tTwo 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 = cd m vertices labeled from 0 to N − 1, where d 2, m 1, and 1 c < d, and two vertices x, y ∈ G(N, d) are adjacent if and only if there is an integer k with 0 kIn this paper, we propose an algorithm to construct multiple independent spanning trees on a recursive circulant graph G(cd m , d) with d > 2, where the number of independent spanning trees matches the connectivity of G(cd m , d).Crown