On vertex-pancyclicity and edge-pancyclicity of the WK-Recursive network

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Abstract

In this paper, we study the pancyclic properties of the WK-Recursive networks. We show that a WK-Recursive network with amplitude W and level L is vertex-pancyclic for W ≥ 6. That is, each vertex on them resides in cycles of all lengths ranging from 3 to N, where N is the size of the interconnection network. On the other hand, we also investigate the m-edge-pancyclicity of the WK-Recursive network. We show that the WK-Recursive network is strictly 3 × 2L-1-edge-pancyclic for W ≥ 7 and L ≥ 1. That is, each edge on them resides in cycles of all lengths ranging from 3 × 2L-1to N; and the value 3 × 2L-1reaches the lower bound of the problem. © 2014 Elsevier Inc. All rights reserved.

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Fang, J. F., & Huang, C. H. (2014). On vertex-pancyclicity and edge-pancyclicity of the WK-Recursive network. Information Sciences, 287, 131–139. https://doi.org/10.1016/j.ins.2014.07.037

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