Strong geodetic number of complete bipartite graphs, crown graphs and hypercubes

Valentin Gledel (1) , Vesna Iršič

1 GOAL - Graphes, AlgOrithmes et AppLications

The strong geodetic number, sg(G), of a graph G is the smallest number of vertices such that by fixing one geodesic between each pair of selected vertices, all vertices of the graph are covered. In this paper, the study of the strong geodetic number of complete bipartite graphs is continued. The formula for sg(K n,m) is given, as well as a formula for the crown graphs S 0 n. Bounds on sg(Q n) are also discussed.

Mots clés: crown graph; geodetic number; complete bipartite graph; strong geodetic number

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Valentin Gledel, Vesna Iršič. Strong geodetic number of complete bipartite graphs, crown graphs and hypercubes. 2018. ⟨hal-01892332⟩