%0 Journal Article 
%A Kuziak, Dorota
%A González Yero, Ismael
%T Further new results on strong resolving partitions for graphs
%D 2020
%@ 2391-5455
%U http://hdl.handle.net/10498/23257
%X 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.
%K strong resolving set
%K strong metric dimension
%K strong resolving partition
%K strong partition dimension
%K strong resolving graph
%~ Universidad de Cádiz