Dual graph (English Wikipedia)

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

Last modified: 23:58:46, 21 September 2026 (UTC)

Ref.Un. Ref.Website

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2221books.google.com

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2218doi.org

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2118ams.org

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43jstor.org

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22wolfram.com

1,091^st place

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22arxiv.org

49^th place

31^st place

22hdl.handle.net

66^th place

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21web.archive.org

1^st place

21rhul.ac.uk

low place

11loc.gov

63^rd place

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11archive.org

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11combinatorics.org

low place

11msri.org

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11math.ca

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11imfm.si

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11nih.gov

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5,148^th place

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ams.org (Global: 434^th place; English: 249^th place)

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 (Global: 6^th place; English: 6^th place)

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 (Global: 49^th place; English: 31^st place)

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 (Global: 3^rd place; English: 3^rd place)

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 (Global: low place; English: low place)

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 (Global: 2^nd place; English: 2^nd place)

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.

hdl.handle.net (Global: 66^th place; English: 34^th place)

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 (Global: low place; English: low place)

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 (Global: 23^rd place; English: 15^th place)

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 (Global: 63^rd place; English: 47^th place)

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 (Global: low place; English: low place)

cms.math.ca

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

msri.org (Global: low place; English: low place)

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 (Global: 5^th place; English: 5^th place)

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 (Global: 5,148^th place; English: 9,757^th place)

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 (Global: low place; English: low place)

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 (Global: 1^st place; English: 1^st place)

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 (Global: 434^th place; English: 249^th place)

mathscinet.ams.org

archive.org (Global: 6^th place; English: 6^th place)

arxiv.org (Global: 49^th place; English: 31^st place)

books.google.com (Global: 3^rd place; English: 3^rd place)

combinatorics.org (Global: low place; English: low place)

doi.org (Global: 2^nd place; English: 2^nd place)

hdl.handle.net (Global: 66^th place; English: 34^th place)

imfm.si (Global: low place; English: low place)

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jstor.org (Global: 23^rd place; English: 15^th place)

loc.gov (Global: 63^rd place; English: 47^th place)

lccn.loc.gov

math.ca (Global: low place; English: low place)

cms.math.ca

msri.org (Global: low place; English: low place)

nih.gov (Global: 5^th place; English: 5^th place)

ncbi.nlm.nih.gov

plus.google.com (Global: 5,148^th place; English: 9,757^th place)

rhul.ac.uk (Global: low place; English: low place)

cs.rhul.ac.uk

web.archive.org (Global: 1^st place; English: 1^st place)

wolfram.com (Global: 1,091^st place; English: 1,169^th place)

mathworld.wolfram.com

Dual graph (English Wikipedia)

ams.org (Global: 434th place; English: 249th place)

mathscinet.ams.org

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 49th place; English: 31st place)

books.google.com (Global: 3rd place; English: 3rd place)

combinatorics.org (Global: low place; English: low place)

doi.org (Global: 2nd place; English: 2nd place)

hdl.handle.net (Global: 66th place; English: 34th place)

imfm.si (Global: low place; English: low place)

preprinti.imfm.si

jstor.org (Global: 23rd place; English: 15th place)

loc.gov (Global: 63rd place; English: 47th place)

lccn.loc.gov

math.ca (Global: low place; English: low place)

cms.math.ca

msri.org (Global: low place; English: low place)

nih.gov (Global: 5th place; English: 5th place)

ncbi.nlm.nih.gov

plus.google.com (Global: 5,148th place; English: 9,757th place)

rhul.ac.uk (Global: low place; English: low place)

cs.rhul.ac.uk

web.archive.org (Global: 1st place; English: 1st place)

wolfram.com (Global: 1,091st place; English: 1,169th place)

mathworld.wolfram.com

ams.org (Global: 434^th place; English: 249^th place)

archive.org (Global: 6^th place; English: 6^th place)

arxiv.org (Global: 49^th place; English: 31^st place)

books.google.com (Global: 3^rd place; English: 3^rd place)

doi.org (Global: 2^nd place; English: 2^nd place)

hdl.handle.net (Global: 66^th place; English: 34^th place)

jstor.org (Global: 23^rd place; English: 15^th place)

loc.gov (Global: 63^rd place; English: 47^th place)

nih.gov (Global: 5^th place; English: 5^th place)

plus.google.com (Global: 5,148^th place; English: 9,757^th place)

web.archive.org (Global: 1^st place; English: 1^st place)

wolfram.com (Global: 1,091^st place; English: 1,169^th place)