The vertex-pancyclicity of the simplified shuffle-cube and the vertex-bipancyclicity of the balanced shuffle-cube
Yasong Liu, Huazhong Lü · International Journal of Computer Mathematics Computer Systems Theory · 2025
A graph G=(V,E) is vertex-pancyclic if for every vertex u and any integer l ranging from 3 to |V|, G contains a cycle C of length l such that u is on C. A bipartite graph G=(V,E) is vertex-bipancyclic if for every vertex u and any even integer l ranging from 4 to |V|, G contains a cycle C of length l such that u is on C. The simplified shuffle-cube and the balanced shuffle-cube, which are two variants of the shuffle-cube and are superior to shuffle-cube in terms of vertex-transitivity. In this paper, we show that the n-dimensional simplified shuffle-cube is vertex-pancyclic for n⩾6, and the n-dimensional balanced shuffle-cube is vertex-bipancyclic for n⩾2.