RT journal article
T1 Further new results on strong resolving partitions for graphs
A1 Kuziak, Dorota
A1 González Yero, Ismael
A2 Estadística e Investigación Operativa
A2 Matemáticas
K1 strong resolving set
K1 strong metric dimension
K1 strong resolving partition
K1 strong partition dimension
K1 strong resolving graph
AB A set W of vertices of a connected graph G strongly resolves two different vertices x, y is not an element of W if either d(G) (x, W) = d(G) (x, y) + d(G) (y, W) or d(G) (y, W) = d(G )(y, x) + d(G) (x, W), where d(G) (x, W) = min{d(x,w): w is an element of W} and d (x,w) represents the length of a shortest x - w path. An ordered vertex partition Pi = {U-1, U-2,...,U-k} of a graph G is a strong resolving partition for G, if every two different vertices of G belonging to the same set of the partition are strongly resolved by some other set of Pi. The minimum cardinality of any strong resolving partition for G is the strong partition dimension of G. In this article, we obtain several bounds and closed formulae for the strong partition dimension of some families of graphs and give some realization results relating the strong partition dimension, the strong metric dimension and the order of graphs.
PB DE GRUYTER
SN 2391-5455
YR 2020
FD 2020-05
LK http://hdl.handle.net/10498/23257
UL http://hdl.handle.net/10498/23257
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026