Geodesic
Enumeration of Labeled Geodetic Graphs with Small Cyclomatic Number
Matematičeskie zametki, Tome 101 (2017) no. 5, pp. 684-689.

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

Explicit expressions for the numbers of labeled geodetic bicyclic, tricyclic, and tetracyclic graphs with a given number of vertices are obtained.
Keywords: geodetic graph, bicyclic graph, tricyclic graph, tetracyclic graph, enumeration. 
@article{MZM_2017_101_5_a3,
     author = {V. A. Voblyi},
     title = {Enumeration of {Labeled} {Geodetic} {Graphs} with {Small} {Cyclomatic} {Number}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {684--689},
     publisher = {mathdoc},
     volume = {101},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a3/}
}
TY  - JOUR
AU  - V. A. Voblyi
TI  - Enumeration of Labeled Geodetic Graphs with Small Cyclomatic Number
JO  - Matematičeskie zametki
PY  - 2017
SP  - 684
EP  - 689
VL  - 101
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a3/
LA  - ru
ID  - MZM_2017_101_5_a3
ER  - 
%0 Journal Article
%A V. A. Voblyi
%T Enumeration of Labeled Geodetic Graphs with Small Cyclomatic Number
%J Matematičeskie zametki
%D 2017
%P 684-689
%V 101
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a3/
%G ru
%F MZM_2017_101_5_a3
V. A. Voblyi. Enumeration of Labeled Geodetic Graphs with Small Cyclomatic Number. Matematičeskie zametki, Tome 101 (2017) no. 5, pp. 684-689. http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a3/

[1] F. Kharari, E. Palmer, Perechislenie grafov, Mir, M., 1977 | MR | Zbl

[2] 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

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

[4] M. Drmota, É. Fusy, M. Kang, V. Kraus, J. Rue, “Asymptotic study of subcritical graph classes”, SIAM J. Discrete Math., 25:4 (2011), 1615–1651 | MR | Zbl

[5] C. E. Frasser, “k-Geodetic graphs and their application to the topological design of computer networks”, Proc. Argentinian Workshop on Theoretical Computer Science, 28 JAIIO-WAIT'99, 1999, 187–203

[6] V. A. Voblyi, “O perechislenii pomechennykh svyaznykh grafov s zadannymi chislami vershin i reber”, Diskretn. analiz i issled. oper., 23:2 (2016), 5–20 | DOI | Zbl

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

[8] Dzh. Riordan, Kombinatornye tozhdestva, Nauka, M., 1982 | MR | Zbl

[9] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady. Elementarnye funktsii, Nauka, M., 1981 | MR | Zbl

[10] V. A. Voblyi, “Perechislenie pomechennykh geodezicheskikh planarnykh grafov”, Matem. zametki, 97:3 (2015), 336–341 | DOI | MR | Zbl

[11] B. R. Heap, “Enumeration homeomorphically irreducible star graphs”, J. Math. Phys., 7 (1966), 1582–1587 | DOI | MR | Zbl

[12] J. G. Stemple, “Geodetic graph homeomorphic to a complete graph”, Combinatorial Mathematics, Ann. New York Acad. Sci., 319, New York Acad. Sci., New York, 1979, 512–517 | DOI | MR | Zbl

[13] P. Hic, “Criticality concepts in geodetic graphs”, Math. Slovaca, 36:3 (1986), 329–333 | MR | Zbl