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

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 =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.
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Bao-Xing Chen, Ji-Xiang Meng, Wen-Jun Xiao. Some new optimal and suboptimal infinite families of undirected double-loop networks. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2006, Vol. 8, pp.299--311. ⟨10.46298/dmtcs.377⟩. ⟨hal-00961120⟩

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