End simplicial vertices in path graphs
Marisa Gutiérrez, Silvia Tondato · Discussiones Mathematicae Graph Theory · 2016
A graph is a path graph if there is a tree, called U V -model, whose vertices are the maximal cliques of the graph and for each vertex x of the graph the set of maximal cliques that contains it induces a path in the tree. A graph is an interval graph if there is a U V -model that is a path, called an interval model. Gimbel [3] characterized those vertices in interval graphs for which there is some interval model where the interval corresponding to those vertices is an end interval. In this work, we give a characterization of those simplicial vertices x in path graphs for which there is some U V -model where the maximal clique containing x is a leaf in this U V -model.