Strong Geodetic Number in Some Networks

Huifen Ge, Zhao Wang and Jinyu Zou

Journal of Mathematics Research, 2019, vol. 11, issue 2, 20-29

Abstract: 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.

Keywords: strong geodetic number; cartesian product; hyper Peterson network; torus network; cube (search for similar items in EconPapers)
Date: 2019
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