Global distribution center number of some graphs and an algorithm

The global center is a newly proposed graph concept. For a graph G  = (V (G ), E (G )), a set S  ⊆ V (G ) is a global distribution center if every vertex v  ∈ V (G )\S is adjacent to a vertex u  ∈ S with |N [u ] ∩ S | ≥ |N [v ] ∩ (V (G )\S )|, where N (v ) = {u  ∈ V (G )|uv  ∈ E (G )} and N [v ] = N (v ) ∪ {v }. The global distribution center number of a graph G is the minimum cardinality of a global distribution center of G . In this paper, we investigate the global distribution center number for special families of graphs. Furthermore, we develop a polynomial time heuristic algorithm to find the set of the global distribution center for general graphs.