Edge metric dimension of some graph operations

2018/09/24 by Peterin, Iztok, Yero, Ismael G.
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.08900

Abstract

Let G=(V, E) be a connected graph. Given a vertex v∈ V and an edge e=uw∈ E, the distance between v and e is defined as d_G(e,v)=min\d_G(u,v),d_G(w,v)\. A nonempty set S⊂ V is an edge metric generator for G if for any two edges e₁,e₂∈ E there is a vertex w∈ S such that d_G(w,e₁)≠ d_G(w,e₂). The minimum cardinality of any edge metric generator for a graph G is the edge metric dimension of G. The edge metric dimension of the join, lexicographic and corona product of graphs is studied in this article.

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