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End Simplicial Vertices in Path Graphs

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Gutierrez M., Tondato S. B.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 2

393-408

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.

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1 Discussiones Mathematicae Graph Theory

1 Gutierrez M.

1 Tondato S. B.

1 2016

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End Simplicial Vertices in Path Graphs