A graph is a path graph if there is a tree, called UV -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 UV -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 UV -model where the maximal clique containing x is a leaf in this UV -model.
@article{bwmeta1.element.doi-10_7151_dmgt_1866,
author = {Marisa Gutierrez and Silvia B. Tondato},
title = {End Simplicial Vertices in Path Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {36},
year = {2016},
pages = {393-408},
zbl = {1334.05126},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1866}
}
Marisa Gutierrez; Silvia B. Tondato. End Simplicial Vertices in Path Graphs. Discussiones Mathematicae Graph Theory, Tome 36 (2016) pp. 393-408. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1866/