Computer Science ›› 2015, Vol. 42 ›› Issue (Z11): 245-246.

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Variety of Conjectures on Group-theoretic Model for Interconnection Networks

SHI Hai-zhong and SHI Yue   

  • Online:2018-11-14 Published:2018-11-14

Abstract: Cayley graph generated by a connected graph was proposed to design certain interconnection networks for supercomputers,on-chip interconnection and data center networks.The conjecture is that let G=(V,E) be a connected graph with node set {1,2,…,n}(n>2) and m edges.If m=2r,then the Cayley graph generated by G is the union of k(0≤k≤r) edge-disjoint Hamiltonian cycles and m-2k perfect matchings.If m=2r+1,then the Cayley graph generated by G is the union of k(0≤k≤r) edge-disjoint Hamiltonian cycles and m-2k perfect matchings.In particular,for k=r and star graph,the conjecture was proposed by Hai-zhong Shi in 1998.

Key words: Cayley graph,Transposition graph,Hamiltonian cycle,Perfect mathching,Conjecture

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