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 6= 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. A recursive circulant graph G(N, d) has N = cdm vertices labeled from 0 to N − 1, where d > 2, m > 1, and 1 6 c < d, and two vertices x, y ∈ G(N, d) are adjacent if and only if there is an integer k with 0 6 k 6 dlogdNe−1 such that x±dk ≡ y (mod N). In this paper, we propose an algorithm to construct multiple independent spanning trees on recursive circulant graphs G(cdm, d) under the condition d > 3, where the number of independent spanning trees matches the connectivity of G(cdm, d).