### Some new optimal and suboptimal infinite families of undirected double-loop networks

*Bao Xing Chen, Ji Xiang Meng, Wen Jun Xiao*

#### Abstract

Let n, s be positive integers such that 2≤s<n and s≠
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) | i ∈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.Full Text: PDF PostScript