Some Properties Of The Complete-transposition Networks And Triangle Tower Networks

Interconnection network is an important part of super computers. When design and select a topological structure for an interconnection network, hamiltonian and fault tolerance is a significant index for evaluating the performance of network, while the conditional connectivity and the restricted connectivity offer metric parameters to measure the reliability of networks. In this paper, we consider the complete-transposition networks and the triangle tower networks obtain the following results:1. We proposed one variety conjectures to show the structure of complete-transposition network. Conjectures as follows: for any integer n≥3, when n=0(mod4) or1(mod4), CTn is a union of k(1≤k≤n(n-1)/4) edge-disjoint Hamiltonian cycles and (n(n-1)/2-2k) perfect matchings. when n=2(mod4) or3(mod4), CTn is a union of k(1≤k≤(n(n-1)-2)/4) edge-disjoint Hamiltonian cycles and (n(n-1)/2-2k) perfect matchings. The paper proved the conjectures are true for n=4, n=5(1≤k≤4) and n=6(1≤k≤6).2. The conditional vertex connectivity and restricted vertex (edge)-connectivity of complete-transposition networks are investigated in this paper. The result of con-ditional vertex connectivity of complete-transposition networks as follows: K1(CTn)=n(n-1)-2for n≥4; K2(CTn)=2n(n-1)-10for n≥5. The result of restricted vertex (edge)-connectivity of complete-transposition networks as follows: when n≥4, K2(CTn)=n(n-1)-2, K3(CTn)=3n(21)/2-6; when n≥3, λ2(CTn)=n(n-1)-2, λ3(CTn)=3n(n-1)/2-4.3. The conditional vertex connectivity and restricted vertex (edge)-connectivity of triangle tower networks are investigated in this paper. The result of conditional vertex connectivity of triangle tower networks as follows: K1(TTn)=4n-8for n≥4；For n=4,κ2(TT4)=8；n≥5,κ2(TTn)=8n-22. The result of restricted vertex(edge)-connectivity of triangle toweer networks as follows when n≥4,κ2(TTn)=4n-8；when n=4,κ3(TT4)=8；when n≥5,κ3(TTn)=6n-15； when n≥3,λ2(TTn)=4n-8,λ3(TTn)=6n-13.