Strong Geodetic Number in Some Networks

  •  Huifen Ge    
  •  Zhao Wang    
  •  Jinyu Zou    


A vertex subset S of a graph is called a strong geodetic set if there exists a choice of exactly one geodesic for each pair of vertices of S in such a way that these (|S| 2) geodesics cover all the vertices of graph G. The strong geodetic number of G, denoted by sg(G), is the smallest cardinality of a strong geodetic set. In this paper, we give an upper bound of strong geodetic number of the Cartesian product graphs and study this parameter for some Cartesian product networks.

This work is licensed under a Creative Commons Attribution 4.0 License.