RT journal article
T1 A note on the metric and edge metric dimensions of 2-connected graphs
A1 Knor, Martin
A1 Škrekovski, Riste
A1 González Yero, Ismael
A2 Matemáticas
K1 Edge metric dimension
K1 Metric dimension
K1 2-connected graphs
K1 Edge subdivision
AB 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 theyuniquely identify the vertices and the edges of G, respectively, by means of distances. Itis 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 issmaller than the metric dimension are already known. In this article, we construct a2-connected graph G such that dim(G) = a and edim(G) = b for every pair of integersa, b, where 4 ≤ b < a. For this we use subdivisions of complete graphs, whose metricdimension 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 subdivisiongraphs under some special conditions.
PB Elsevier
SN 0166-218X
YR 2021
FD 2021-03-04
LK http://hdl.handle.net/10498/29430
UL http://hdl.handle.net/10498/29430
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 22-sep-2026