Vertex-pancyclism in the generalized sum of digraphs

A digraph D=(V(D),A(D)) of order n≥3 is pancyclic, whenever D contains a directed cycle length k for each k∈{3,…,n}; and vertex-pancyclic iff, vertex v∈V(D) k∈{3,…,n}, passing through v. Let D1, D2, …, Dk be collection pairwise disjoint digraphs. The generalized sum (g.s.) Dk, denoted by ⊕i=1kDi or D1⊕D2⊕⋯⊕Dk, the set all digraphs satisfying: (i) V(D)=⋃i=1kV(Di), (ii) D〈V(Di)〉≅Di i=1,2,…,k, (iii) pair vertices belonging to different summands D, there exactly one arc between them, with an arbitrary but fixed direction. in will called Dk. Hamiltonian digraphs, this paper we give simple sufficient conditions D∈⊕i=1kDi vertex-pancyclic. This result extends obtained Cordero-Michel et al. (2016).