Marc Noy, Clément Requilé, Juanjo Rué,
"Enumeration of labeled 4-regular planar graphs"
, in Electronic Notes in Discrete Mathematics, Vol. 61, Seite(n) 933-939, 8-2017, ISSN: 1571-0653
Enumeration of labeled 4-regular planar graphs
Sprache des Titels:
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.