k次十二面体–师连通圈网络

K Dodecahedron-Shi Connected Cycles Networks

摘要: 互连网络是超级计算机的重要组成部分，片上互连网络是当前研究的热点课题之一。k次十二面体–师连通圈网络是一类重要的互连网络，是在2010年师海忠提出互联网络的正则图连通圈网络模型的基础上设计的新网络模型。它是将十二面体连通圈网络的每个顶点用三角形代替k次得到的，记为DSCC(k)，它是3正则3连通的平面图，且有许多好的性质。文中提出了关于该网络的一系列猜想，如猜想1：k次十二面体–师连通圈网络是Hamilton图，对猜想1、2、3作了严格的证明。作者还利用图的笛卡尔乘积方法构建了新的笛卡尔乘积互连网络DSCC(k)xK₂和DSCC(k)xC_m，并对其性质进行了研究。

Abstract: An interconnection network is an important part of a supercomputer. On chip interconnection network is one of the hot topics in current research. A class of important interconnection network of the K dodecahedron-Shi connected cycle network is a new network model based on the regular graph connected cycle network model of the internet in 2010. It is obtained by replacing each vertex of a dodecahedron connected cycle network with triangle K times, and it is recorded as DSCC(k). It is a 3-regular and 3-connected plane graph, and has many good properties. In this paper, a series of conjectures about the network are proposed, such as the conjecture 1: K dodecahedron-Shi connected cycle network is a Hamilton graph, and the conjectures 1, 2, and 3 are proved strictly. The author also uses the Descartes product method of graphs to construct a new Descartes product interconnected DSCC(k)xK₂ and DSCC(k)xC_m, and study their properties.