Enumeration of labeled 4-regular planar graphs

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Title:	Enumeration of labeled 4-regular planar graphs
Author:	Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
Abstract:	© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract:	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.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -generating functions -graph enumeration -planar graphs -Classificació AMS::05 Combinatorics::05C Graph theory
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Submitted version Article
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