本文提出并分析了一种新的互连网络—三角塔网络．当n>4或n=4时，它是极大连通的，紧超连通的，即三角塔网络的连通度κ(T Tn)是2n−3．星网络是三角塔网络的子网络，故而三角塔网络除了继承星网络的很多优良性质(例如：点对称性、连通性、点可迁性等)，还说明Sn能以膨胀数1嵌入T Tn．当三角塔网络和超立方体与冒泡排序网络有近乎相同的顶点数时，三角塔网络的直径和连通度与超立方体与冒泡排序网络的直径和连通度相比直径更小、连通度更大．本文给出了三角塔网络的直径和平均距离，并提出了关于三角塔网络Hamilton性的一簇猜想，并且证明这个猜想对于n=3,4以及n=5,6, k=1,2时是正确的．%In this paper, we propose and analyze a new interconnection network called trian-gle tower graphetwork. It is maximally connected and tightly super-connected, for n>4 or n = 4, i.e. the connectivity κ(T Tn) of T Tn is 2n−3. The star graph is a specific subgraph of the proposed triangle tower graph. Therefore, the triangle tower graph not only inherits many good capabilities possessed by the star graph (e.g., vertex symmetry, connectivity, vertex transition, etc.), but also shows that Sn can be embedded into T Tn with digit 1. The proposed triangle tower graph is superior to the traditional hypercube and bubble-sort graph with respect to diameter, connectivity and conditional vertex connectivity as that these three graphs have approximately similar numbers of vertices. The diameter and average distance are presented for the proposed network. We also propose one variety conjectures on Hamiltonicity of triangle tower graph and prove conjectures are true for n=3, 4 and n=5, 6, k=1, 2.
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