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 u v and x y 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 , u v ∈ E (C 1) and x y ∈ E (C 2). In this paper, we prove that the n -star graph S n 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. [ABSTRACT FROM AUTHOR]