On the edge metric dimension for the random graph

Abstract

Let $G(V,E)$ be a connected simple undirected graph. In this paper we prove that the edge metric dimension (introduced by Kelenc, Tratnik and Yero) of the Erdős-Rényi random graph $G(n,p)$ is given by: $$\text{edim}(G(n,p))=(1+o(1))\frac{4\log (n)}{\log (1/q)},$$ where $q=1-2p(1-p{)}^2(2-p)$.