We prove that ℳm is the graph having as vertices all the perfect matchings in the point set Pn whose edges are straight line segments and do not cross, and that it has no Hamilton path for m odd, m>3.Expand

This work is devoted to evaluating the so-called metric dimension of a finite connected graph for a number of graph families, as long as to study its behavior with respect to the join and the cartesian product of graphs.Expand

A vertex v is a boundary vertex of a connected graph G if there exists a vertex u such that no neighbor of v is further away from u than v. This paper is devoted to study these kinds of vertices for the family of chordal graphs.Expand

In this paper, we exhibit a simple local transformation for which the following polygon classes are connected: monotone, x-monotones, star-shaped, (weakly) edge-visible and ( weakly) externally visible.Expand