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

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Abstract

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 vr 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 N1, where d2, m1, and 1c<d, and two vertices x,yG(N,d) are adjacent if and only if there is an integer k with 0klogdN1 such that x±dky (mod N). In this paper, we propose an algorithm to construct multiple independent spanning trees on a recursive circulant graph G(cdm,d) with d>2, where the number of independent spanning trees matches the connectivity of G(cdm,d).

Keywords

Recursive circulant graphs
Independent spanning trees
Internally disjoint paths
Fault-tolerant broadcasting
Secure message distribution

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This research was partially supported by National Science Council under the Grants NSC96–2218–E–141–001.