Enumeration of labeled 4-regular planar graphs

In this extended abstract, we present the first combinatorial scheme for counting labeled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function counting labeled 4-regular planar graphs can be computed effectively as the s...

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Bibliographic Details
Published in:Electronic notes in discrete mathematics Vol. 61; pp. 933 - 939
Main Authors: Noy, Marc, Requilé, Clément, Rué, Juanjo
Format: Journal Article Publication
Language:English
Published: Elsevier B.V 01.08.2017
Subjects:
05 Combinatorics
05C Graph theory
Classificació AMS
generating functions
graph enumeration
Matemàtiques i estadística
planar graphs
Àrees temàtiques de la UPC
generating functions
planar graphs
graph enumeration
ISSN:1571-0653, 1571-0653
Online Access:Get full text
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Summary:In this extended abstract, we present the first combinatorial scheme for counting labeled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function counting labeled 4-regular planar graphs can be computed effectively as the solution of a system of equations. From here we can extract the coefficients by means of algebraic calculus. As a by-product, we can also compute the algebraic generating function counting labeled 3-connected 4-regular planar maps.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2017.07.056