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Constructing Edge-Disjoint Spanning Trees in Product Networks
March 2003 (vol. 14 no. 3)
pp. 213-221

Abstract—A Cartesian product network is obtained by applying the cross operation on two graphs. In this paper, we study the problem of constructing the maximum number of edge-disjoint spanning trees (abbreviated to EDSTs) in Cartesian product networks. Let G=(V_G, E_G) be a graph having n_1 EDSTs and F=(V_F, E_F) be a graph having n_2 EDSTs. Two methods are proposed for constructing EDSTs in the Cartesian product of G and F , denoted by G\times F . The graph G has t_1=|E_G|-n_1(|V_G|-1) more edges than that are necessary for constructing n_1 EDSTs in it, and the graph F has t_2=|E_F|-n_2(|V_F|-1) more edges than that are necessary for constructing n_2 EDSTs in it. By assuming that t_1\ge n_1 and t_2 \ge n_2 , our first construction shows that n_1+ n_2 EDSTs can be constructed in G \times F . Our second construction does not need any assumption and it constructs n_1 + n_2-1 EDSTs in G \times F . By applying the proposed methods, it is easy to construct the maximum numbers of EDSTs in many important Cartesian product networks, such as hypercubes, tori, generalized hypercubes, mesh connected trees, and hyper Petersen networks.

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Index Terms:
Cartesian product networks, edge-disjoint trees, spanning trees, embedding, fault-tolerance, interconnection networks.
Shan-Chyun Ku, Biing-Feng Wang, Ting-Kai Hung, "Constructing Edge-Disjoint Spanning Trees in Product Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 14, no. 3, pp. 213-221, March 2003, doi:10.1109/TPDS.2003.1189580
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