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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
Rebuilding convex sets in graphs
(2005)
The usual distance between pairs of vertices in a graph naturally gives rise to the notion of an interval between a pair of vertices in a graph. This in turn allows us to extend the notions of convex sets, convex hull, and ...
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
Towards a new framework for domination
(2011)
Dominating concepts constitute a cornerstone in Graph Theory. Part of the efforts in the field have been focused in finding different mathematical frameworks where domination notions naturally arise, providing new points ...
Artículo
Steiner distance and convexity in graphs
(2008)
We use the Steiner distance to define a convexity in the vertex set of a graph, which has a nice behavior in the well-known class of HHD-free graphs. For this graph class, we prove that any Steiner tree of a vertex set is ...