2024/09/21 by Liu, Yasong, Huazhong Lü, Lü, Huazhong
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Approximation and Integration #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2409.14015
openalex publication_date 2024/09/21 · openalex created_date 2024/10/25 · openalex updated_date 2026/07/28
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\geqslant 6, and the n-dimensional balanced shuffle-cube is vertex-bipancyclic for n\geqslant 2.