RT journal article
T1 On the vertices belonging to all edge metric bases
A1 Hakanen, Anni
A1 Junnila, Ville
A1 Laihonen, Tero
A1 González Yero, Ismael
A2 Matemáticas
K1 Edge metric dimension
K1 Edge metric basis
K1 Edge basis forced vertices
K1 Metric dimension
K1 Metric basis
AB An edge metric basis of a connected graph G is a smallest possible set of vertices S ofG satisfying the following: for any two edges e, f of G there is a vertex s ∈ S such thatthe distances from s to e and f differ. The cardinality of an edge metric basis is the edgemetric dimension of G. In this article we consider the existence of vertices in a graphG such that they must belong to each edge metric basis of G, and we call them edgebasis forced vertices. On the other hand, we name edge void vertices those vertices whichdo not belong to any edge metric basis. Among other results, we first deal with thecomputational complexity of deciding whether a given vertex is an edge basis forcedvertex or an edge void vertex. We also establish some tight bounds on the numberof edge basis forced vertices of a graph, as well as, on the number of edges in a graphhaving at least one edge basis forced vertex. Moreover, we show some realization resultsconcerning which values for the integers n, k and f allow to confirm the existence of agraph G with n vertices, f edge basis forced vertices and edge metric dimension k.
PB Elsevier
SN 0166-218X
YR 2025
FD 2025
LK http://hdl.handle.net/10498/39037
UL http://hdl.handle.net/10498/39037
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 09-may-2026