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

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 × 2 L −1 -edge-pancyclic for W  ⩾ 7 and L  ⩾ 1. That is, each edge on them resides in cycles of all lengths ranging from 3 × 2 L −1 to N ; and the value 3 × 2 L −1 reaches the lower bound of the problem.

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