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 Erd\H{o}s-R\'enyi random graph $G(n, p)$ is given by: $$\textrm{edim}(G(n, p)) = (1 + o(1))\frac{4\log(n)}{\log(1/q)},$$ where $q = 1 - 2p(1-p)^2(2-p)$.