圈网中的几个问题

Several Problems in Loop Networks

圈网Ｇ（Ｎ；１，ｓ２，ｓ３，…，ｓｋ）［１］在局域网的设计和实现中是一种很流行的网．解决了圈网中的以下几个问题：１）求出了Ｇ（Ｎ；１，ｓ２）的更好的直径上界，及Ｇ（Ｎ；１，ｓ２，ｓ３）的直径上界；２）给出了Ｇ（Ｎ；１，ｓ２）的任两顶点间的距离公式，及Ｇ（Ｎ；１，ｓ２）的任两顶点间的最短路由算法；３）在ｓｉ（ｉ＝１，２，…，ｋ，ｓ１＝１）满足一定条件下，求出了Ｇ（Ｎ；１，ｓ２，ｓ３，…，ｓｋ）的连通度和边－连通度，并证得它比１９６２年Ｈａｒａｒｙ构造的可靠通信网更具一般性。

Loop network G(N;1,s 2,s 3,…,s k) has been one of the most popular network topologies used in the design and implemantation of local area networks.Such several problems are solved:1)We obtain a better upper bound of diameter of G(N;1,s 2) and a upper bound of diameter of G(N;1,s 2,s 3). 2)The shortest routing algrithm in G(N;1,s 2) is developed by our defining the distance formular between any two vertices.3)We obtain the connectivity and edge-connetivity of G(N;1,s 2,s 3,…,s k) when every s i(i=1,2,…,k,s 1=1) meets some condition,and prove that such a G(N;1,s 2,s 3,…,s k) is more general and regular than the reliable communication network constructed by Harary in 1962.