双环网络直径点和宽直径点的分布特性  

Distribution Attribution of Diameter Node and Width Diameter Nodefor Double-loop Networks

作　　者：方木云[1] 侯海金[1] 吴爱清[1] 刘明[1] 

机构地区：[1]安徽工业大学计算机学院,安徽马鞍山243032

出　　处：《小型微型计算机系统》2013年第4期749-752,共4页Journal of Chinese Computer Systems

基　　金：安徽省教育厅重大基金项目(ZD2008005-1)资助

摘　　要：针对单个有向单位步长双环网络G(N;1,h),根据其直径和宽直径的定义,并借助其等价L形瓦进行直径和宽直径路由的构造,证明了任意双环网络的直径点和宽直径点均小于或等于2个;证明了直径点一定分布在L形瓦的第一象限内,宽直径点一定分布在L形瓦的两个坐标轴上.对于一族有向单位步长双环网络G(N;1,2≤h≤N-1),随着步长h的递增,该族双环网络路由的节点顺序具有由小到大变为由大到小的特点,借助VB6.0编程仿真了该族双环网络直径点和宽直径点的分布图,发现其直径点和宽直径点具有波动下降的特征;直径点往往大于宽直径点;步长h在中间处两者的值最大;对于某个双环网络,如果直径点有两个,则其宽直径点必有两个.As for each double-loop network G（N; 1 ,h）, based on its definitions of diameter and wide diameter, and by aid of routing for diameter and wide diameter in its equivalent L-tile, it is founded that the sum of diameter node and wide diameter node for each double-loop network is respectively smaller than or equal to 2, and that the diameter node must locate in the first Quadrant, while the wide diameter node must locate on the x Axis or y Axis. As for double-loop network family G（N; 1,2≤h≤N-1 ）, by the increasing of step h, the value of its serial routing node has the characteristic of from small to big and then from big to small. By the aid of using vb6.0 to simulate the distribution diagram of diameter node and wide diameter node, it is founded that the value of diameter node and wide diameter node has the characteristic of fluctuating down, and that diameter node value is often bigger than wide diameter node value, and that they both reach biggest when step in the middle, and that as for one double-loop network, if there exist two diameter nodes then there must exist two wide diameter nodes.

关 键 词：双环网络 直径 宽直径 直径点 宽直径点 

分 类 号：O157.9[理学—数学] TP302[理学—基础数学]