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

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−1 to N; and the value 3 × 2L−1 reaches the lower bound of the problem.