@misc{10498/29430,
year = {2021},
month = {3},
url = {http://hdl.handle.net/10498/29430},
abstract = {For a given graph G, the metric and edge metric dimensions of G, dim(G) and edim(G),
are the cardinalities of the smallest possible subsets of vertices in V(G) such that they
uniquely identify the vertices and the edges of G, respectively, by means of distances. It
is already known that metric and edge metric dimensions are not in general comparable.
Infinite families of graphs with pendant vertices in which the edge metric dimension is
smaller than the metric dimension are already known. In this article, we construct a
2-connected graph G such that dim(G) = a and edim(G) = b for every pair of integers
a, b, where 4 ≤ b < a. For this we use subdivisions of complete graphs, whose metric
dimension is in some cases smaller than the edge metric dimension. Along the way,
we present an upper bound for the metric and edge metric dimensions of subdivision
graphs under some special conditions.},
publisher = {Elsevier},
keywords = {Edge metric dimension},
keywords = {Metric dimension},
keywords = {2-connected graphs},
keywords = {Edge subdivision},
title = {A note on the metric and edge metric dimensions of 2-connected graphs},
doi = {10.1016/j.dam.2021.02.020},
author = {Knor, Martin and Škrekovski, Riste and González Yero, Ismael},
}