An asymptotics for the number of labelled planar tetracyclic and pentacyclic graphs
Prikladnaâ diskretnaâ matematika, no. 1 (2023), pp. 72-79
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A connected graph with a cyclomatic number $k$ is said to be a $k$-cyclic graph. We obtain the formula for the number of labelled non-planar pentacyclic graphs with a given number of vertices, and find the asymptotics of the number of labelled connected planar tetracyclic and pentacyclic graphs with $n$ vertices as $n\to\infty$. We prove that under a uniform probability distribution on the set of graphs under consideration, the probability that the labelled tetracyclic graph is planar is asymptotically equal to 1089/1105, and the probability that the labeled pentacyclic graph is planar is asymptotically equal to 1591/1675.
Keywords:
labelled graph, planar graph, tetracyclic graph, pentacyclic graph, block, enumeration, asymptotics, probability.
V. A. Voblyi. An asymptotics for the number of labelled planar tetracyclic and pentacyclic graphs. Prikladnaâ diskretnaâ matematika, no. 1 (2023), pp. 72-79. http://geodesic.mathdoc.fr/item/PDM_2023_1_a3/
@article{PDM_2023_1_a3,
author = {V. A. Voblyi},
title = {An asymptotics for the number of labelled planar tetracyclic and pentacyclic graphs},
journal = {Prikladna\^a diskretna\^a matematika},
pages = {72--79},
year = {2023},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/PDM_2023_1_a3/}
}