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Enumeration of labeled 4-regular planar graphs

Author
Noy, M.; Requile, C.; Rue, J.
Type of activity
Journal article
Journal
Electronic notes in discrete mathematics
Date of publication
2017-08-01
Volume
61
First page
933
Last page
939
DOI
https://doi.org/10.1016/j.endm.2017.07.056 Open in new window
Repository
http://hdl.handle.net/2117/109823 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S1571065317302214?via%3Dihub Open in new window
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-co...
Citation
Noy, M., Requile, C., Rue, J. Enumeration of labeled 4-regular planar graphs. "Electronic notes in discrete mathematics", 1 Agost 2017, vol. 61, p. 933-939.
Keywords
generating functions, graph enumeration, planar graphs
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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