Parameters on distance of undirected toroidal mesh
Xin Xie · 2012
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.