On the edge metric dimension for the random graph

2016/12/21 by Zubrilina, Nina
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.06936

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: \textrmedim(G(n, p)) = (1 + o(1))(4log(n))/(log(1/q)), where q = 1 - 2p(1-p)²(2-p).

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• Metric dimension for random graphs
• The Metric Dimension of Sparse Random Graphs
• On Edge Dimension of a Graph
• Metric dimension and edge metric dimension of unicyclic graphs
• Graphs with the edge metric dimension smaller than the metric dimension