https://hal.inria.fr/hal-00961120Chen, Bao-XingBao-XingChenDepartment of computer science [Zhangzhou] - Zhangzhou Teachers CollegeCollege of Mathematics & System Science [Xinjiang] - Xinjiang UniversityMeng, Ji-XiangJi-XiangMengCollege of Mathematics & System Science [Xinjiang] - Xinjiang UniversityXiao, Wen-JunWen-JunXiaoDepartment of computer science [Guangzhou] - SUSTech - Southern University of Science and Technology [Shenzhen]Some new optimal and suboptimal infinite families of undirected double-loop networksHAL CCSD2006[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Inria Sophia Antipolis-Méditerranée / I3s, Service Ist2014-03-19 15:48:532019-10-15 11:00:042014-03-19 16:11:49enJournal articleshttps://hal.inria.fr/hal-00961120/document10.46298/dmtcs.377application/pdf1Let 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 =Zn={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.