Metric dimension for random graphs

Bela Bollobas (1) , Dieter Mitsche (2) , Pawel Pralat (3)

1 DAMTP - Department of Applied Mathematics and Theoretical Physics
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 Department of Mathematics

The metric dimension of a graph $G$ is the minimum number of vertices in a subset $S$ of the vertex set of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $S$. In this paper we investigate the metric dimension of the random graph $G(n,p)$ for a wide range of probabilities $p=p(n)$.

Mots clés: metric dimension; random graphs

Domaines: Combinatoire [math.CO]

Bela Bollobas, Dieter Mitsche, Pawel Pralat. Metric dimension for random graphs. The Electronic Journal of Combinatorics, 2013, 20 (4), pp.P52. ⟨hal-00914127⟩