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Artículo
Resolving sets for Johnson and Kneser graphs
(2013)
A set of vertices SS in a graph GG is a resolving set for GG if, for any two vertices u,vu,v, there exists x∈Sx∈S such that the distances d(u,x)≠d(v,x)d(u,x)≠d(v,x). In this paper, we consider the Johnson graphs J(n,k)J(n,k) ...
Artículo
Artículo
On the metric dimension, the upper dimension and the resolving number of graphs
(2013)
This paper deals with three resolving parameters: the metric dimension, the upper dimension and the resolving number. We first answer a question raised by Chartrand and Zhang asking for a characterization of the graphs ...
Artículo
The difference between the metric dimension and the determining number of a graph
(2014)
We study the maximum value of the difference between the metric dimension and the determining number of a graph as a function of its order. We develop a technique that uses functions related to locating-dominating sets to ...
Artículo
The determining number of Kneser graphs
(2013)
A set of vertices S is a determining set of a graph G if every automorphism of G is uniquely determined by its action on S. The determining number of G is the minimum cardinality of a determining set of G. This paper studies ...
Artículo
The resolving number of a graph
(2013)
We study a graph parameter related to resolving sets and metric dimension, namely the resolving number, introduced by Chartrand, Poisson and Zhang. First, we establish an important difference between the two parameters: ...