The number of labeled block-cactus graphs
Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 2, pp. 24-32.

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

We obtain exact and asymptotical formulas for the number of block-cactus graphs and eulerian block-cactus graphs with the given number of vertices. Tab. 1, bibliogr. 15.
Keywords: enumeration, block graph, block-cactus graph, asymptotics.
Mots-clés : cactus
@article{DA_2014_21_2_a1,
     author = {V. A. Voblyi and A. K. Meleshko},
     title = {The number of labeled block-cactus graphs},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {24--32},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2014_21_2_a1/}
}
TY  - JOUR
AU  - V. A. Voblyi
AU  - A. K. Meleshko
TI  - The number of labeled block-cactus graphs
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2014
SP  - 24
EP  - 32
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2014_21_2_a1/
LA  - ru
ID  - DA_2014_21_2_a1
ER  - 
%0 Journal Article
%A V. A. Voblyi
%A A. K. Meleshko
%T The number of labeled block-cactus graphs
%J Diskretnyj analiz i issledovanie operacij
%D 2014
%P 24-32
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2014_21_2_a1/
%G ru
%F DA_2014_21_2_a1
V. A. Voblyi; A. K. Meleshko. The number of labeled block-cactus graphs. Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 2, pp. 24-32. http://geodesic.mathdoc.fr/item/DA_2014_21_2_a1/

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

[2] Voblyi V. A., “Perechislenie pomechennykh eilerovykh kaktusov”, Mat. XI Mezhdunar. seminara “Diskretnaya matematika i eë prilozheniya”, MGU, M., 2012, 275–277

[3] Voblyi V. A., Meleshko A. K., “Perechislenie pomechennykh eilerovykh polnoblochnykh grafov”, Mat. XV Mezhvuz. seminara “Kombinatornye konfiguratsii i ikh prilozheniya” (Kirovograd, 2013), Izd-vo Kirovogradskogo nats. tekh. un-ta, Kirovograd, 2013, 15–18

[4] Zykov A. A., Osnovy teorii grafov, Nauka, M., 1987, 382 pp. | MR | Zbl

[5] Prudnikov A. P. i dr., Integraly i ryady, v. 1, Nauka, M., 1981, 800 pp. | MR | Zbl

[6] Tatt U., Teoriya grafov, Mir, M., 1988, 424 pp. | MR

[7] Kharari F., Palmer E., Perechislenie grafov, Mir, M., 1977, 324 pp. | MR

[8] Carlitz L., “Single variable Bell polynomials”, Collect. Math., 14 (1962), 13–25 | MR | Zbl

[9] Flajolet Ph., Sedgewick R., Analytic combinatorics, Cambridge Univ. Press, Cambridge, 2009, 810 pp. | MR | Zbl

[10] Ford G. W., Uhlenbeck G. E., “Combinatorial problems in theory graphs. I”, Proc. Nat. Acad. Sci. USA, 42 (1956), 13–25 | DOI | MR

[11] Husimi K., “Note on Mayer's theory of cluster integrals”, J. Chem. Phys., 18 (1950), 682–684 | DOI | MR

[12] Lan J. K., Chang G. J., “Algorithmic aspects of $k$-domination in graphs”, Discrete Appl. Math., 161 (2013), 1513–1520 | DOI | MR

[13] Leroux P., “Enumerative problems inspired by Mayer's theory of cluster integrals”, Electron. J. Comb., 11 (2004), No 32 | MR

[14] Randerath B., Volkmann L., “A characterization of well covered block-cactus graphs”, Australasian J. Comb., 9 (1994), 307–314 | MR | Zbl

[15] Wang F.-H., Wang Y.-L., Chang J.-M., “The lower and upper forcing geodetic numbers of block-cactus graphs”, Eur. J. Oper. Res., 175 (2006), 238–245 | DOI | MR | Zbl