Constructing Independent Spanning Trees on Generalized Recursive Circulant Graphs

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,...

On Constructing Three Edge Independent Spanning Trees

Abstract. In this paper, we show that a prior result by Khuller and Schieber on the construction of k edge independent spanning trees in a k edge-connected graph fails under certain scenarios. We illustrate the failing of the algorithm with an example and identify the cause, which we refer to as the partial order inversion. For the case of k = 3, we develop a method to compute three edge indepe...

The number of spanning trees in circulant graphs

The Asymptotic Number of Spanning Trees in Circulant Graphs

Let T (G) be the number of spanning trees in graph G. In this note we explore the asymptotics of T (G) for circulant graphs. The circulant graph Cs1,s2,···,sk n is the 2k regular graph with n vertices labelled 0, 1, 2, · · · , n − 1, where node i has the 2k neighbors, (0 ≤ i ≤ n − 1) adjacent to vertices i + s1, i + s2, · · · , i + sk mod n. In this note we give a closed formula for the asympto...

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 ...