Geodesic
Enumeration of labeled Eulerian pentacyclic graphs
Prikladnaâ diskretnaâ matematika, no. 4 (2020), pp. 87-92

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

An Euler graph is a connected graph in which all degrees of vertices are even numbers. A pentacyclic graph is a connected graph with $n$ vertices and $n + 4$ edges. We obtain an explicit formula for the number of labeled Euler pentacyclic graphs with a given number of vertices, and found the corresponding asymptotics for the number of such graphs with a large number of vertices. We prove that, given a uniform probability distribution, the probability that a labeled pentacyclic Euler graph is a block (cactus) is asymptotically $53/272$ ($63/272$), respectively.
Keywords: labeled graph, Eulerian graph, pentacyclic graph, block, enumeration, asymptotics, probability. 
@article{PDM_2020_4_a5,
     author = {V. A. Voblyi},
     title = {Enumeration of labeled {Eulerian} pentacyclic graphs},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {87--92},
     publisher = {mathdoc},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2020_4_a5/}
}
TY  - JOUR
AU  - V. A. Voblyi
TI  - Enumeration of labeled Eulerian pentacyclic graphs
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2020
SP  - 87
EP  - 92
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2020_4_a5/
LA  - ru
ID  - PDM_2020_4_a5
ER  - 
%0 Journal Article
%A V. A. Voblyi
%T Enumeration of labeled Eulerian pentacyclic graphs
%J Prikladnaâ diskretnaâ matematika
%D 2020
%P 87-92
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2020_4_a5/
%G ru
%F PDM_2020_4_a5
V. A. Voblyi. Enumeration of labeled Eulerian pentacyclic graphs. Prikladnaâ diskretnaâ matematika, no. 4 (2020), pp. 87-92. http://geodesic.mathdoc.fr/item/PDM_2020_4_a5/