Geodesic
Enumeration of Labeled Geodetic Planar Graphs
Matematičeskie zametki, Tome 97 (2015) no. 3, pp. 336-341.

Voir la notice de l'article provenant de la source Math-Net.Ru

The labeled geodetic outerplanar and planar graphs with a prescribed number of vertices are enumerated and an asymptotic formula for the number of such graphs with a large number of vertices is obtained.
Keywords: geodetic graph, planar graph, number of vertices, asymptotics, labeled graphs. 
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V. A. Voblyi. Enumeration of Labeled Geodetic Planar Graphs. Matematičeskie zametki, Tome 97 (2015) no. 3, pp. 336-341. http://geodesic.mathdoc.fr/item/MZM_2015_97_3_a1/

[1] J. G. Stemple, M. E. Watkins, “On planar geodetic graphs”, J. Combin. Theory, 4 (1968), 101–117 | MR | Zbl

[2] V. A. Voblyi, “Ob odnoi formule dlya chisla pomechennykh svyaznykh grafov”, Diskretn. analiz i issled. oper., 19:4 (2012), 48–59 | MR

[3] Ya. Gulden, D. Dzhekson, Perechislitelnaya kombinatorika, Nauka, M., 1990 | MR | Zbl

[4] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady. V 3 t. T. 1. Elementarnye funktsii, Fizmatlit, M., 2003 | Zbl

[5] Ph. Flajolet, R. Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, Cambridge, 2009 | MR | Zbl

[6] I. Plesník, “Two construction of geodetic graphs”, Math. Slovaca, 27:1 (1977), 65–71 | MR | Zbl

[7] B. Zelinka, “Geodetic graphs which are homeomorphic to complete graphs”, Math. Slovaca, 27:2 (1977), 129–132 | MR | Zbl

[8] G. W. Ford, G. E. Uhlenbeck, “Combinatorial problems in theory graphs. IV”, Proc. Nat. Acad. Sci. U.S.A., 43 (1957), 163–167 | DOI | MR

[9] K. A. Rybnikov, Vvedenie v kombinatornyi analiz, Izd-vo Mosk. un-ta, M., 1985 | MR | Zbl