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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 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: ...
Artículo
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
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
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 ...