Geodesic
Asymptotical enumeration of some abeled geodetic graphs
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 58-67

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

We asymptotically enumerate labeled geodetic $k$-cyclic cacti and obtain asymptotics for the numbers of labeled connected geodetic unicyclic, bicyclic, and tricyclic $n$-vertex graphs. We prove that under the uniform probability distribution, the probabilities that a random labeled connected unicyclic, bicyclic, or tricyclic graph is a geodetic graph are asymptotically equal to $1/2$, $3/20$, and $1/30$, respectively. In addition, we prove that almost all labeled connected geodetic tricyclic graphs are cacti.
Keywords: enumeration, labeled graph, geodetic graph, $k$-cyclic graph, asymptotics, random graph.
Mots-clés : cactus 
@article{INTO_2022_215_a5,
     author = {V. A. Voblyi},
     title = {Asymptotical enumeration of some abeled geodetic graphs},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {58--67},
     publisher = {mathdoc},
     volume = {215},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_215_a5/}
}
TY  - JOUR
AU  - V. A. Voblyi
TI  - Asymptotical enumeration of some abeled geodetic graphs
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 58
EP  - 67
VL  - 215
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_215_a5/
LA  - ru
ID  - INTO_2022_215_a5
ER  - 
%0 Journal Article
%A V. A. Voblyi
%T Asymptotical enumeration of some abeled geodetic graphs
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 58-67
%V 215
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_215_a5/
%G ru
%F INTO_2022_215_a5
V. A. Voblyi. Asymptotical enumeration of some abeled geodetic graphs. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 58-67. http://geodesic.mathdoc.fr/item/INTO_2022_215_a5/