The Journal of the Indian Mathematical Society

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Outerplanar Graphs and Weak Duals


Affiliations
1 Institute for Advanced Study, India
2 Austrian Academy of Sciences, SUNY at Binghamton, United States
3 University of Oxford, United Kingdom
     

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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 K4 or K2,3. 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.
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  • Outerplanar Graphs and Weak Duals

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Authors

Herbert J. Fleischner
Institute for Advanced Study, India
Dennis P. Geller
Austrian Academy of Sciences, SUNY at Binghamton, United States
Frank Harary
University of Oxford, United Kingdom

Abstract


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 K4 or K2,3. 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.