On Well-Covered Quadrangulations

Arthur S.Finbow1, Bert L.Hartnell1, Michael D.Plummer2
1Department of Mathematics and Computing Science Saint Mary’s University Halifax, Canada B3H 3C3
2Department of Mathematics Vanderbilt University Nashville, TN 37240

Abstract

A graph \( G \) is said to be well-covered if every maximal independent set of vertices has the same cardinality. A planar (simple) graph in which each face is a quadrilateral is called a (planar) quadrangulation. In the present paper, we characterize those planar quadrangulations which are well-covered.