摘要
平均距离μ(G),距离控制数γl(G)和距离独立数αd(G)是度量网络性能的重要参数.n维无向超环面网是超立方体的推广.证明了μ(G)=1/d1d2…dn-1n∑i=1(ei2+ei+ei'2-ei'/2·d1d2…dn/di),γ(G)=2当且仅当[e1'+e2'…+en'/2]≤l≤d(G)-1(d1≥d2≥…dn≥4),以及αd(G)=2当[d1+d2+…+dn-2/3]≤d≤d(G)-1(d1≥d2≥…dn≥3).
The average distance μ（G）,distance l-domination number γl（G） and distance d-independence number αd（G） are important parameters to measure the performance of a network.The n-dimensional undirected toroidal mesh C（d1,d2,…,dn） is considered as a generalization of hypercube.It was proved that μ（C（d1,d2,…,dn））=1/d1d2…dn-1n∑i=1（ei2＋ei＋ei＇2-ei＇/2·d1d2…dn/di）,γ（C（d1,d2,…,dn））=2 if and only if[e1＇＋e2＇…＋en＇/2]≤l≤d（G）-1 for d1≥d2≥…dn≥4,and αd（G）=2 for [d1＋d2＋…＋dn-2/3]≤d≤d（G）-1（d1≥d2≥…dn≥3.
基金
Supported by Foundation of Huangshan University(2011xkj012)
关键词
平均距离
距离控制数
距离独立数
无向超环面网
average distance
distance domination number
distance independence number
undirected toroidal mesh
