Hamiltonian Decomposition of 2r-regular Graph Connected Cycles Networks
An Interconnection network is an important part of a supercomputer.The interconnection network is often modeled as an undirected graph,in which the vertices correspond to processor/communication parts,and the edges correspond to communication channels.In 2010,Hai-zhong Shi proposed the model of 2r-regular graph connected cycles,for designing analyzing and improving such networks,and proposed many conjectures.In this paper,we proved that any 2r-regular graph-connected cycles network is a union of edge-disjoint Hamiltonian cycle and a perfect matching.Therefore,we proved that the conjectures are true when primitive graphs are 2r-regular connected graph.
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