Geodesic
Enumeration of Labeled Bicyclic and Tricyclic Eulerian Graphs
Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 678-683 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Explicit formulas for the number of labeled bicyclic and tricyclic Eulerian graphs and for the number of labeled tricyclic Eulerian blocks are obtained. Many-vertex asymptotics for these numbers are found.
Keywords: labeled Eulerian graph, bicyclic Eulerian graph, tricyclic Eulerian graph, Eulerian block, enumeration of graphs, generating function. 
@article{MZM_2012_92_5_a3,
     author = {V. A. Voblyi},
     title = {Enumeration of {Labeled} {Bicyclic} and {Tricyclic} {Eulerian} {Graphs}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {678--683},
     year = {2012},
     volume = {92},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a3/}
}
TY  - JOUR
AU  - V. A. Voblyi
TI  - Enumeration of Labeled Bicyclic and Tricyclic Eulerian Graphs
JO  - Matematičeskie zametki
PY  - 2012
SP  - 678
EP  - 683
VL  - 92
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a3/
LA  - ru
ID  - MZM_2012_92_5_a3
ER  - 
%0 Journal Article
%A V. A. Voblyi
%T Enumeration of Labeled Bicyclic and Tricyclic Eulerian Graphs
%J Matematičeskie zametki
%D 2012
%P 678-683
%V 92
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a3/
%G ru
%F MZM_2012_92_5_a3
V. A. Voblyi. Enumeration of Labeled Bicyclic and Tricyclic Eulerian Graphs. Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 678-683. http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a3/

[1] R. C. Read, “Euler graphs on labelled nodes”, Canad. J. Math., 14 (1962), 482–486 | DOI | MR | Zbl

[2] S. Tazawa, Y.-L. Jin, T. Shirakura, “Enumeration of labelled 2-connected Euler graphs”, J. Combin. Inform. System Sci., 23:1-4 (1998), 407–414 | MR | Zbl

[3] F. Kharari, Teoriya grafov, Mir, M., 1973 | MR | Zbl

[4] 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

[5] V. E. Stepanov, “O nekotorykh osobennostyakh stroeniya sluchainogo grafa vblizi kriticheskoi tochki”, TVP, 32:4 (1987), 633–657 | MR | Zbl

[6] E. F. Dmitriev, Perechislenie otmechennykh dvutsvetnykh svyaznykh grafov s nebolshim tsiklomaticheskim chislom, Dep. v VINITI No 4959-85

[7] V. A. Voblyi, “O perechislenii pomechennykh svyaznykh bitsiklicheskikh i tritsiklicheskikh grafov bez mostov”, Matem. zametki, 91:2 (2012), 308–311

[8] V. N. Sachkov, Vvedenie v kombinatornye metody diskretnoi matematiki, MTsNMO, M., 2004

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