Dual graph (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Dual graph" in English language version.

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21books.google.com

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1archive.org

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1combinatorics.org

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mathscinet.ams.org

Bóna, Miklós (2006), A walk through combinatorics (2nd ed.), World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, p. 276, doi:10.1142/6177, ISBN 981-256-885-9, MR 2361255.
Servatius, Brigitte; Christopher, Peter R. (1992), "Construction of self-dual graphs", The American Mathematical Monthly, 99 (2): 153–158, doi:10.2307/2324184, JSTOR 2324184, MR 1144356.
Angelini, Patrizio; Bläsius, Thomas; Rutter, Ignaz (2014), "Testing mutual duality of planar graphs", International Journal of Computational Geometry and Applications, 24 (4): 325–346, arXiv:1303.1640, doi:10.1142/S0218195914600103, MR 3349917.
Cho, Jung Jin; Chen, Yong; Ding, Yu (2007), "On the (co)girth of a connected matroid", Discrete Applied Mathematics, 155 (18): 2456–2470, doi:10.1016/j.dam.2007.06.015, MR 2365057.
Noy, Marc (2001), "Acyclic and totally cyclic orientations in planar graphs", American Mathematical Monthly, 108 (1): 66–68, doi:10.2307/2695680, JSTOR 2695680, MR 1857074.
Gabow, Harold N. (1995), "Centroids, representations, and submodular flows", Journal of Algorithms, 18 (3): 586–628, doi:10.1006/jagm.1995.1022, MR 1334365
Tutte, W. T. (1984), Graph theory, Encyclopedia of Mathematics and its Applications, vol. 21, Reading, MA: Addison-Wesley Publishing Company, Advanced Book Program, p. 289, ISBN 0-201-13520-5, MR 0746795.
Riley, T. R.; Thurston, W. P. (2006), "The absence of efficient dual pairs of spanning trees in planar graphs", Electronic Journal of Combinatorics, 13 (1): Note 13, 7, doi:10.37236/1151, MR 2255413.
Lyons, Russell (1998), "A bird's-eye view of uniform spanning trees and forests", Microsurveys in discrete probability (Princeton, NJ, 1997), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 41, Amer. Math. Soc., Providence, RI, pp. 135–162, MR 1630412. See in particular pp. 138–139.
Harary, Frank (1969), Graph Theory, Reading, Mass.: Addison-Wesley Publishing Co., Theorem 9.4, p. 142, MR 0256911.
Welsh, D. J. A. (1969), "Euler and bipartite matroids", Journal of Combinatorial Theory, 6 (4): 375–377, doi:10.1016/s0021-9800(69)80033-5, MR 0237368.
Florek, Jan (2010), "On Barnette's conjecture", Discrete Mathematics, 310 (10–11): 1531–1535, doi:10.1016/j.disc.2010.01.018, MR 2601261.
Las Vergnas, Michel (1980), "Convexity in oriented matroids", Journal of Combinatorial Theory, Series B, 29 (2): 231–243, doi:10.1016/0095-8956(80)90082-9, MR 0586435.
Fleischner, Herbert J.; Geller, D. P.; Harary, Frank (1974), "Outerplanar graphs and weak duals", Journal of the Indian Mathematical Society, 38: 215–219, MR 0389672.
Nakamoto, Atsuhiro; Negami, Seiya (2000), "Full-symmetric embeddings of graphs on closed surfaces", Memoirs of Osaka Kyoiku University, 49 (1): 1–15, MR 1833214.
Pisanski, Tomaž; Randić, Milan (2000), "Bridges between geometry and graph theory" (PDF), in Gorini, Catherine A. (ed.), Geometry at Work, MAA Notes, vol. 53, Cambridge University Press, pp. 174–194, ISBN 9780883851647, MR 1782654
Jones, G. A.; Thornton, J. S. (1983), "Operations on maps, and outer automorphisms", Journal of Combinatorial Theory, Series B, 35 (2): 93–103, doi:10.1016/0095-8956(83)90065-5, MR 0733017
Whitney, Hassler (1931), "A theorem on graphs", Annals of Mathematics, Second Series, 32 (2): 378–390, doi:10.2307/1968197, JSTOR 1968197, MR 1503003.

archive.org

Tutte, W. T. (1984), Graph theory, Encyclopedia of Mathematics and its Applications, vol. 21, Reading, MA: Addison-Wesley Publishing Company, Advanced Book Program, p. 289, ISBN 0-201-13520-5, MR 0746795.

arxiv.org

Angelini, Patrizio; Bläsius, Thomas; Rutter, Ignaz (2014), "Testing mutual duality of planar graphs", International Journal of Computational Geometry and Applications, 24 (4): 325–346, arXiv:1303.1640, doi:10.1142/S0218195914600103, MR 3349917.
Eppstein, David (2003), "Dynamic generators of topologically embedded graphs", Proceedings of the 14th ACM/SIAM Symposium on Discrete Algorithms, pp. 599–608, arXiv:cs.DS/0207082.

books.google.com

Bóna, Miklós (2006), A walk through combinatorics (2nd ed.), World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, p. 276, doi:10.1142/6177, ISBN 981-256-885-9, MR 2361255.
Thulasiraman, K.; Swamy, M. N. S. (2011), Graphs: Theory and Algorithms, John Wiley & Sons, Exercise 7.11, p. 198, ISBN 978-1-118-03025-7.
Nishizeki, Takao; Chiba, Norishige (2008), Planar Graphs: Theory and Algorithms, Dover Books on Mathematics, Dover Publications, p. 16, ISBN 978-0-486-46671-2.
Foulds, L. R. (2012), Graph Theory Applications, Springer, pp. 66–67, ISBN 978-1-4612-0933-1.
Bondy, Adrian; Murty, U.S.R. (2008), "Planar Graphs", Graph Theory, Graduate Texts in Mathematics, vol. 244, Springer, Theorem 10.28, p. 267, doi:10.1007/978-1-84628-970-5, ISBN 978-1-84628-969-9, LCCN 2007923502
Nishizeki, Takao; Chiba, Norishige (2008), Planar Graphs: Theory and Algorithms, Dover Books on Mathematics, Dover Publications, Theorem 1.1, p. 8, ISBN 978-0-486-46671-2
Diestel, Reinhard (2006), Graph Theory, Graduate Texts in Mathematics, vol. 173, Springer, p. 25, ISBN 978-3-540-26183-4.
Godsil, Chris; Royle, Gordon F. (2013), Algebraic Graph Theory, Graduate Texts in Mathematics, vol. 207, Springer, Theorem 14.3.1, p. 312, ISBN 978-1-4613-0163-9.
Oxley, J. G. (2006), Matroid Theory, Oxford Graduate Texts in Mathematics, vol. 3, Oxford University Press, p. 93, ISBN 978-0-19-920250-8.
Lyons, Russell (1998), "A bird's-eye view of uniform spanning trees and forests", Microsurveys in discrete probability (Princeton, NJ, 1997), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 41, Amer. Math. Soc., Providence, RI, pp. 135–162, MR 1630412. See in particular pp. 138–139.
Gross, Jonathan L.; Yellen, Jay, eds. (2003), Handbook of Graph Theory, CRC Press, p. 724, ISBN 978-1-58488-090-5.
Samet, Hanan (2006), Foundations of Multidimensional and Metric Data Structures, Morgan Kaufmann, p. 348, ISBN 978-0-12-369446-1.
Oxley, J. G. (2006), "5.2 Duality in graphic matroids", Matroid Theory, Oxford graduate texts in mathematics, vol. 3, Oxford University Press, p. 143, ISBN 978-0-19-920250-8.
Tutte, W. T. (2012), Graph Theory As I Have Known It, Oxford Lecture Series in Mathematics and Its Applications, vol. 11, Oxford University Press, p. 87, ISBN 978-0-19-966055-1.
Chorley, Richard J.; Haggett, Peter (2013), Integrated Models in Geography, Routledge, p. 646, ISBN 978-1-135-12184-6.
Kandel, Abraham; Bunke, Horst; Last, Mark (2007), Applied Graph Theory in Computer Vision and Pattern Recognition, Studies in Computational Intelligence, vol. 52, Springer, p. 16, ISBN 978-3-540-68020-8.
Devadoss, Satyan L.; O'Rourke, Joseph (2011), Discrete and Computational Geometry, Princeton University Press, p. 111, ISBN 978-1-4008-3898-1.
Piguet, Christian (2004), "7.2.1 Static CMOS Logic", Low-Power Electronics Design, CRC Press, pp. 7-1 – 7-2, ISBN 978-1-4200-3955-9.
Kaeslin, Hubert (2008), "8.1.4 Composite or complex gates", Digital Integrated Circuit Design: From VLSI Architectures to CMOS Fabrication, Cambridge University Press, p. 399, ISBN 978-0-521-88267-5.
Richeson, David S. (2012), Euler's Gem: The Polyhedron Formula and the Birth of Topology, Princeton University Press, pp. 58–61, ISBN 978-1-4008-3856-1.
Biggs, Norman; Lloyd, E. Keith; Wilson, Robin J. (1998), Graph Theory, 1736–1936, Oxford University Press, p. 118, ISBN 978-0-19-853916-2.

combinatorics.org

Riley, T. R.; Thurston, W. P. (2006), "The absence of efficient dual pairs of spanning trees in planar graphs", Electronic Journal of Combinatorics, 13 (1): Note 13, 7, doi:10.37236/1151, MR 2255413.

doi.org

Bóna, Miklós (2006), A walk through combinatorics (2nd ed.), World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, p. 276, doi:10.1142/6177, ISBN 981-256-885-9, MR 2361255.
Servatius, Brigitte; Christopher, Peter R. (1992), "Construction of self-dual graphs", The American Mathematical Monthly, 99 (2): 153–158, doi:10.2307/2324184, JSTOR 2324184, MR 1144356.
Bondy, Adrian; Murty, U.S.R. (2008), "Planar Graphs", Graph Theory, Graduate Texts in Mathematics, vol. 244, Springer, Theorem 10.28, p. 267, doi:10.1007/978-1-84628-970-5, ISBN 978-1-84628-969-9, LCCN 2007923502
Angelini, Patrizio; Bläsius, Thomas; Rutter, Ignaz (2014), "Testing mutual duality of planar graphs", International Journal of Computational Geometry and Applications, 24 (4): 325–346, arXiv:1303.1640, doi:10.1142/S0218195914600103, MR 3349917.
Cho, Jung Jin; Chen, Yong; Ding, Yu (2007), "On the (co)girth of a connected matroid", Discrete Applied Mathematics, 155 (18): 2456–2470, doi:10.1016/j.dam.2007.06.015, MR 2365057.
Hartvigsen, D.; Mardon, R. (1994), "The all-pairs min cut problem and the minimum cycle basis problem on planar graphs", SIAM Journal on Discrete Mathematics, 7 (3): 403–418, doi:10.1137/S0895480190177042.
Noy, Marc (2001), "Acyclic and totally cyclic orientations in planar graphs", American Mathematical Monthly, 108 (1): 66–68, doi:10.2307/2695680, JSTOR 2695680, MR 1857074.
Gabow, Harold N. (1995), "Centroids, representations, and submodular flows", Journal of Algorithms, 18 (3): 586–628, doi:10.1006/jagm.1995.1022, MR 1334365
Riley, T. R.; Thurston, W. P. (2006), "The absence of efficient dual pairs of spanning trees in planar graphs", Electronic Journal of Combinatorics, 13 (1): Note 13, 7, doi:10.37236/1151, MR 2255413.
He, Xin (1999), "On floor-plan of plane graphs", SIAM Journal on Computing, 28 (6): 2150–2167, doi:10.1137/s0097539796308874.
Welsh, D. J. A. (1969), "Euler and bipartite matroids", Journal of Combinatorial Theory, 6 (4): 375–377, doi:10.1016/s0021-9800(69)80033-5, MR 0237368.
Florek, Jan (2010), "On Barnette's conjecture", Discrete Mathematics, 310 (10–11): 1531–1535, doi:10.1016/j.disc.2010.01.018, MR 2601261.
Las Vergnas, Michel (1980), "Convexity in oriented matroids", Journal of Combinatorial Theory, Series B, 29 (2): 231–243, doi:10.1016/0095-8956(80)90082-9, MR 0586435.
Jones, G. A.; Thornton, J. S. (1983), "Operations on maps, and outer automorphisms", Journal of Combinatorial Theory, Series B, 35 (2): 93–103, doi:10.1016/0095-8956(83)90065-5, MR 0733017
Whitney, Hassler (1932), "Non-separable and planar graphs", Transactions of the American Mathematical Society, 34 (2): 339–362, doi:10.1090/S0002-9947-1932-1501641-2, PMC 1076008.
Du, Qiang; Gunzburger, Max (2002), "Grid generation and optimization based on centroidal Voronoi tessellations", Applied Mathematics and Computation, 133 (2–3): 591–607, doi:10.1016/S0096-3003(01)00260-0.
Rippmann, Matthias (2016), Funicular Shell Design: Geometric Approaches to Form Finding and Fabrication of Discrete Funicular Structures, Habilitation thesis, Diss. ETH No. 23307, ETH Zurich, pp. 39–40, doi:10.3929/ethz-a-010656780, hdl:20.500.11850/116926. See also Erickson, Jeff (June 9, 2016), Reciprocal force diagrams from Nouvelle Méchanique ou Statique by Pierre de Varignon (1725), Is this the oldest illustration of duality between planar graphs?.
Whitney, Hassler (1931), "A theorem on graphs", Annals of Mathematics, Second Series, 32 (2): 378–390, doi:10.2307/1968197, JSTOR 1968197, MR 1503003.

handle.net

hdl.handle.net

Flammini, Alessandro (October 1996), Scaling Behavior for Models of River Network, Ph.D. thesis, International School for Advanced Studies, pp. 40–41.
Rippmann, Matthias (2016), Funicular Shell Design: Geometric Approaches to Form Finding and Fabrication of Discrete Funicular Structures, Habilitation thesis, Diss. ETH No. 23307, ETH Zurich, pp. 39–40, doi:10.3929/ethz-a-010656780, hdl:20.500.11850/116926. See also Erickson, Jeff (June 9, 2016), Reciprocal force diagrams from Nouvelle Méchanique ou Statique by Pierre de Varignon (1725), Is this the oldest illustration of duality between planar graphs?.

imfm.si

preprinti.imfm.si

Pisanski, Tomaž; Randić, Milan (2000), "Bridges between geometry and graph theory" (PDF), in Gorini, Catherine A. (ed.), Geometry at Work, MAA Notes, vol. 53, Cambridge University Press, pp. 174–194, ISBN 9780883851647, MR 1782654

jstor.org

Servatius, Brigitte; Christopher, Peter R. (1992), "Construction of self-dual graphs", The American Mathematical Monthly, 99 (2): 153–158, doi:10.2307/2324184, JSTOR 2324184, MR 1144356.
Noy, Marc (2001), "Acyclic and totally cyclic orientations in planar graphs", American Mathematical Monthly, 108 (1): 66–68, doi:10.2307/2695680, JSTOR 2695680, MR 1857074.
Whitney, Hassler (1931), "A theorem on graphs", Annals of Mathematics, Second Series, 32 (2): 378–390, doi:10.2307/1968197, JSTOR 1968197, MR 1503003.

loc.gov

lccn.loc.gov

Bondy, Adrian; Murty, U.S.R. (2008), "Planar Graphs", Graph Theory, Graduate Texts in Mathematics, vol. 244, Springer, Theorem 10.28, p. 267, doi:10.1007/978-1-84628-970-5, ISBN 978-1-84628-969-9, LCCN 2007923502

math.ca

cms.math.ca

Tutte, William Thomas (1953), A contribution to the theory of chromatic polynomials

msri.org

Lyons, Russell (1998), "A bird's-eye view of uniform spanning trees and forests", Microsurveys in discrete probability (Princeton, NJ, 1997), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 41, Amer. Math. Soc., Providence, RI, pp. 135–162, MR 1630412. See in particular pp. 138–139.

nih.gov

ncbi.nlm.nih.gov

Whitney, Hassler (1932), "Non-separable and planar graphs", Transactions of the American Mathematical Society, 34 (2): 339–362, doi:10.1090/S0002-9947-1932-1501641-2, PMC 1076008.

plus.google.com

Rippmann, Matthias (2016), Funicular Shell Design: Geometric Approaches to Form Finding and Fabrication of Discrete Funicular Structures, Habilitation thesis, Diss. ETH No. 23307, ETH Zurich, pp. 39–40, doi:10.3929/ethz-a-010656780, hdl:20.500.11850/116926. See also Erickson, Jeff (June 9, 2016), Reciprocal force diagrams from Nouvelle Méchanique ou Statique by Pierre de Varignon (1725), Is this the oldest illustration of duality between planar graphs?.

rhul.ac.uk

cs.rhul.ac.uk

Gagarin, Andrei; Kocay, William; Neilson, Daniel (2003), "Embeddings of small graphs on the torus" (PDF), Cubo, 5: 351–371, archived from the original (PDF) on 2017-02-01, retrieved 2015-08-12.

web.archive.org

Gagarin, Andrei; Kocay, William; Neilson, Daniel (2003), "Embeddings of small graphs on the torus" (PDF), Cubo, 5: 351–371, archived from the original (PDF) on 2017-02-01, retrieved 2015-08-12.

Dual graph (English Wikipedia)

ams.org

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archive.org

arxiv.org

books.google.com

combinatorics.org

doi.org

handle.net

hdl.handle.net

imfm.si

preprinti.imfm.si

jstor.org

loc.gov

lccn.loc.gov

math.ca

cms.math.ca

msri.org

nih.gov

ncbi.nlm.nih.gov

plus.google.com

rhul.ac.uk

cs.rhul.ac.uk

web.archive.org

wolfram.com

mathworld.wolfram.com