基于FQ_n和圈的细胞分裂生长网络FQCC(n,k)及其性质

Based on FQ_n and Cycles Cell-Breeding Network FQCC(n,k) and Its Properties

摘要: 折叠立方体连通圈网络FQCC(n) (n > 1)是一类典型的互连网络，它是3正则的。师海忠根据折叠立方体连通圈网络i>FQCC(n) (n > 1)和细胞分裂生长图模型设计出了一种新的互连网络——FQCC(n,k) (n > 1，k是非负整数)：用三长的圈代替FQCC(n)的每个顶点且圈中每个顶点恰位于折叠立方体连通圈网络FQCC(n) (n > 1)中与该顶点关联的一条边上，得到新的网络FQCC(n,1)；再类似的用三长的圈代替FQCC(n,1)的每个顶点得FQCC(n,2)，循环执行上述方法k次得到的新网络称为FQCC(n,k) (n > 1，k是非负整数)。该网络FQCC(n,k)在保持了FQCC(n)的小的固定的度(为3)的特性外，还有比FQCC(n)更好的扩展性。进而提出了猜想：FQCC(n,k)是Hamilton图。赵媛证明了FQCC(2,k)是平面图和Hamilton图，还证明了FQCC(n,k) (k > 1)不是点可迁的。

Abstract: The folded cube-connected cycles network FQCC(n) (n > 1) is a classic interconnection network; it is 3 regular. On the basis of the folded cube-connected cycles network FQCC(n) (n > 1) and cell- breeding graph model for interconnection network, FQCC(n,k) (n > 1, k is not a negative integer) is designed by Haizhong Shi: each vertex in the folded cube-connected cycles network FQCC(n) (n > 1) is replaced by the cycles of length 3, and the vertex in every cycle is located on the edge of the folded cube-connected cycles connected to the vertex, then we called the new network FQCC(n,1); in similar way each vertex in the folded cube-connected cycles network FQCC(n,1) (n > 1) is replaced by the cycles of length 3, then we called the new network FQCC(n,2), looping execution the above method k times, and then get the new network—FQCC(n,k) (n > 1, k is not a negative integer). The network FQCC(n,k) keeps small or fixed degree (is 3) of FQCC(n), and has better extendability than FQCC(n). Furthermore proposed a conjecture: FQCC(n,k) is Hamiltonian. Yuan Zhao proofs that FQCC(2,k) is planar and Hamiltonian, and that FQCC(n,k) (k > 1) is not vertex- transitive.