Asymptotic enumeration of perfect matchings in m-barrel fullerene graphs

A connected plane cubic graph is called an m-barrel fullerene and denoted by F(m,k), if it has the following structure: The first circle is an m-gon. Then the m-gon is bounded by m pentagons. After that we have additional k layers of hexagons between circles. At the last circle we have a layer of m-...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 266; pp. 153 - 162
Main Authors Behmaram, Afshin, Boutillier, Cédric
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 15.08.2019
Elsevier BV
Elsevier
Subjects
Asymptotic methods
Asymptotic properties
Combinatorics
Enumeration
Fullerene graph
Fullerenes
Graphs
Hexagons
m-barrel fullerene
Mathematics
Perfect matchings
m-barrel fullerene
Fullerene graph
Perfect matchings
05C70
15A15 perfect matchings
fullerene graph
2010 Mathematics Subject Classification. 05C30
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Summary:A connected plane cubic graph is called an m-barrel fullerene and denoted by F(m,k), if it has the following structure: The first circle is an m-gon. Then the m-gon is bounded by m pentagons. After that we have additional k layers of hexagons between circles. At the last circle we have a layer of m-pentagons connected to the second m-gon. In this paper we asymptotically count by two different methods the number of perfect matchings in m-barrel fullerene graphs, as the number of hexagonal layers is large.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2018.08.012