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The Tutte Polynomial Characterizes Simple Outerplanar Graphs

Published online by Cambridge University Press:  09 March 2011

A. J. GOODALL ,
A. de MIER ,
S. D. NOBLE  and
M. NOY
A. J. GOODALL
Affiliation:
Department of Applied Mathematics and Institute of Theoretical Computer Science, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic (e-mail: goodall.aj@googlemail.com)
A. de MIER
Affiliation:
Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain (e-mail: anna.de.mier@upc.edu, marc.noy@upc.edu)
S. D. NOBLE
Affiliation:
Department of Mathematical Sciences, Brunel University, Kingston Lane, Uxbridge UB8 3PH, UK (e-mail: steven.noble@brunel.ac.uk)
M. NOY
Affiliation:
Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain (e-mail: anna.de.mier@upc.edu, marc.noy@upc.edu)
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Abstract

We show that if G is a simple outerplanar graph and H is a graph with the same Tutte polynomial as G, then H is also outerplanar. Examples show that the condition of G being simple cannot be omitted.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 4 , July 2011 , pp. 609 - 616
Copyright
Copyright © Cambridge University Press 2011

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