Previous article Next article On the Maximum Order of the Automorphism Group of a Planar Triply Connected GraphLouis WeinbergLouis Weinberghttps://doi.org/10.1137/0114062PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Oystein Ore, Theory of graphs, American Mathematical Society Colloquium Publications, Vol. XXXVIII, American Mathematical Society, Providence, R.I., 1962x+270 MR0150753 (27:740) 0105.35401 CrossrefGoogle Scholar[2] Sundaram Seshu and , Myril B. Reed, Linear graphs and electrical networks, Addison-Wesley Series in the Engineering Sciences, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961x+315 MR0147120 (26:4638) 0102.34001 Google Scholar[3] Hassler Whitney, 2-Isomorphic Graphs, Amer. J. Math., 55 (1933), 245–254 MR1506961 CrossrefGoogle Scholar[4] Hassler Whitney, Congruent Graphs and the Connectivity of Graphs, Amer. J. Math., 54 (1932), 150–168 MR1506881 0003.32804 CrossrefGoogle Scholar[5] H. Whitney, Nonseparable and planar graphs, Trans. Amer. Math. Soc., 34 (1931), 339–362 CrossrefGoogle Scholar[6] Louis Weinberg, Plane representations and codes for planar graphsProc. Third Annual Allerton Conf. on Circuit and System Theory, Univ. Illinois, Urbana, Ill., 1965, 733–744 MR0244093 (39:5410) Google Scholar[7] L. Weinberg, A simple and efficient algorithm for determining isomorphism of planar triply connected graphs, IEEE Trans. Circuit Theory, CT-13 (1966), to appear Google Scholar[8] W. T. Tutte, A census of planar maps, Canad. J. Math., 15 (1963), 249–271 MR0146823 (26:4343) 0115.17305 CrossrefISIGoogle Scholar[9] R. Frucht, Die Gruppe des Petersenschen Graphen und der Kantensysteme der regulären Polyeder, Comment. Math. Helv., 9 (1937), 217–223 10.1007/BF01258190 0016.37601 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Thermodynamics, dynamics, and structure of supercritical water at extreme conditions1 January 2020 | Physical Chemistry Chemical Physics, Vol. 22, No. 28 Cross Ref Distribution of Topological Types in Grain-Growth Microstructures29 June 2020 | Physical Review Letters, Vol. 125, No. 1 Cross Ref Finding new grain forms in three dimensions31 January 2019 | Scientific Reports, Vol. 9, No. 1 Cross Ref Topological generalization of the rigid-nonrigid transition in soft-sphere and hard-sphere fluids6 May 2019 | Physical Review E, Vol. 99, No. 5 Cross Ref Polyhedron and Polychoron Codes for Describing Atomic Arrangements16 January 2018 Cross Ref VoroTop : Voronoi cell topology visualization and analysis toolkit14 December 2017 | Modelling and Simulation in Materials Science and Engineering, Vol. 26, No. 1 Cross Ref Matrix description of the complete topology of three-dimensional cells10 May 2016 | Scientific Reports, Vol. 6, No. 1 Cross Ref Topological framework for local structure analysis in condensed matter12 October 2015 | Proceedings of the National Academy of Sciences, Vol. 112, No. 43 Cross Ref A Fourier-theoretic approach for inferring symmetriesComputational Geometry, Vol. 47, No. 2 Cross Ref Statistical topology of three-dimensional Poisson-Voronoi cells and cell boundary networks20 December 2013 | Physical Review E, Vol. 88, No. 6 Cross Ref Complete Topology of Cells, Grains, and Bubbles in Three-Dimensional Microstructures30 August 2012 | Physical Review Letters, Vol. 109, No. 9 Cross Ref An Introduction to Surface Topology Cross Ref References Cross Ref Weinberg bounds over nonspherical graphsJournal of Graph Theory, Vol. 33, No. 4 Cross Ref Isomorphism, Unification, and Term-Rewriting Systems Cross Ref A SimpleO(logN) Time Parallel Algorithm for Testing Isomorphism of Maximal Outerplanar GraphsJournal of Parallel and Distributed Computing, Vol. 56, No. 2 Cross Ref Robuste und effiziente Erkennung von 3D Objekten mittels Hypergraph-Homomorphismen Cross Ref Linear Time Automorphism Algorithms for Trees, Interval Graphs, and Planar GraphsCharles J. Colbourn and Kellogg S. Booth13 July 2006 | SIAM Journal on Computing, Vol. 10, No. 1AbstractPDF (2616 KB)The uniquely embeddable planar graphsDiscrete Mathematics, Vol. 4, No. 4 Cross Ref References Cross Ref A Simple and Efficient Algorithm for Determining Isomorphism of Planar Triply Connected GraphsIEEE Transactions on Circuit Theory, Vol. 13, No. 2 Cross Ref Volume 14, Issue 4| 1966SIAM Journal on Applied Mathematics History Submitted:14 December 1964Accepted:15 March 1966Published online:03 August 2006 InformationCopyright © 1966 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0114062Article page range:pp. 729-738ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics