CAJ | 학술논문

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．
본문제출병분석료일충신적호련망락—삼각탑망락．당n>4혹n=4시，타시겁대련통적，긴초련통적，즉삼각탑망락적련통도κ(T Tn)시2n?3．성망락시삼각탑망락적자망락，고이삼각탑망락제료계승성망락적흔다우량성질(례여：점대칭성、련통성、점가천성등)，환설명Sn능이팽창수1감입T Tn．당삼각탑망락화초립방체여모포배서망락유근호상동적정점수시，삼각탑망락적직경화련통도여초립방체여모포배서망락적직경화련통도상비직경경소、련통도경대．본문급출료삼각탑망락적직경화평균거리，병제출료관우삼각탑망락Hamilton성적일족시상，병차증명저개시상대우n=3,4이급n=5,6, k=1,2시시정학적．
In this paper, we propose and analyze a new interconnection network called trian-gle tower graph/network. 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.