Outerplanar Graphs and Weak Duals
Herbert Fleischner, Dennis P. Geller, Frank Harary · Journal of the Indian Mathematical Society · 1974
A planar graph is outer planar if it can be embedded irr the plane so that every point lies on the exterior region. Outerplanar graphs were characterized by Chartrand and Harary [1] as those graphs containing subgraphs homeomorphic onto K 4 or K 2,3 . In this paper we present an alternate characterization of outerplanar graphs in terms of duals, and discuss some relationships between the degrees of the points of outerplanar graphs and the lengths of the boundaries of their interior regions.