Some new optimal and suboptimal infinite families of undirected double-loop networks
Let n, s be positive integers such that 2 <= s <= n and s not equal n 2. An undirected double- loop network G( n; 1, s) is an undirected graph ( V, E), where V = Z(n)={0, 1, 2, ... , n-1} and E={( i, i+1 (mod n)), (i, i+s (mod n)) vertical bar i is an element of Z}. It is a circulant graph with n nodes and degree 4. In this paper, the sufficient and necessary conditions for a class of undirected double- loop networks to be optimal are presented. By these conditions, 6 new optimal and 5 new suboptimal infinite families of undirected double- loop networks are given.
optimal suboptimal undirected double-loop networks diameter