Two-disjoint-cycle-cover edge/vertex bipancyclicity of star graphs

A bipartite graph G is two-disjoint-cycle-cover edge [r(1),r(2)]-bipancyclic if, for any vertex-disjoint edges uv and xy in G and any even integer l satisfying r(1) <= l <= r(2), there exist vertex-disjoint cycles C-1 and C-2 such that |V(C-1)| = l, |V(C-2)| = |V(G)| - l, uv is an element of E(C-1) and xy is an element of E(C-2). In this paper, we prove that the n-star graph Sn is two-disjoint-cycle-cover edge [6,n!/2]-bipancyclic for n >= 5, and thus it is two-disjoint-cycle-cover vertex [6,n!/2]-bipancyclic for n >= 5. Additionally, it is examined that S-n is two-disjoint-cycle-cover [6,n!/2]-bipancyclic for n >= 4. (c) 2024 Published by Elsevier B.V.