Enumeration of Labeled Series-Parallel Tricyclic Graphs

A series-parallel graph is a graph that does not contain a complete graph with four vertices as a minor. An explicit formula for the number of labeled series-parallel tricyclic graphs with a given number of vertices is obtained, and the corresponding asymptotics for the number of such graphs with a...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 275; no. 6; pp. 778 - 782
Main Author Voblyi, V. A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 02.10.2023
Springer
Springer Nature B.V
Subjects
Apexes
Asymptotic properties
Enumeration
Graph theory
Graphs
Mathematics
Mathematics and Statistics
series-parallel graph
enumeration
labeled graph
asymptotics
probability
05C30
Online AccessGet full text
ISSN1072-3374
1573-8795
DOI10.1007/s10958-023-06720-7

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Summary:A series-parallel graph is a graph that does not contain a complete graph with four vertices as a minor. An explicit formula for the number of labeled series-parallel tricyclic graphs with a given number of vertices is obtained, and the corresponding asymptotics for the number of such graphs with a large number of vertices is found. We prove that under a uniform probability distribution, the probability that the labeled tricyclic graph is a series-parallel graph is asymptotically equal to 13 / 15.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06720-7