Chromatic sums of general maps on the sphere and the projective plane
type: Item
instance of: scholarly article
title: Chromatic sums of general maps on the sphere and the projective plane
zbMATH Open document ID: 1114.05048
author: Yanpei Liu
author: ZhaoXiang Li
published in: Discrete Mathematics
publication date: 2007-02-02T00:00:00Z
review text: The chromatic sum function of a class of rooted maps is the sum of the chromatic polynomials of all these maps with a given root-vertex degree, root-face degree and number of edges, non-root vertices and non-root faces, multiplied by a monomial in five variables that enumerate these parameters. Authors' absstract: We study the chromatic sum functions of rooted general maps on the sphere and the projective plane. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of rooted loopless maps, bipartite maps and Eulerian maps are also derived. Moreover, some explicit expressions of enumerating functions are also derived. Reviewer's remark: Among these explicit expressions are formulas for the number of rooted loopless maps, bipartite maps and Eulerian maps on the sphere. These three formulas are already in the literature, but only the first one is given a citation in this article.
Mathematics Subject Classification ID: 05C30
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 5121350
zbMATH Keywords: chromatic sum function
zbMATH Keywords: rooted maps
zbMATH Keywords: planar
zbMATH Keywords: projective planar
zbMATH Keywords: enumerating function
zbMATH Keywords: Eulerian maps
reviewed by: Timothy R. S. Walsh
MaRDI profile type: Publication
full work available at URL: j.disc.2006.05.039
OpenAlex ID: W2051481624
cites work: Asymptotic Methods in Enumeration
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cites work: Chromatic polynomials for regular graphs and modified wheels
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cites work: Chromatic Sums for Rooted Planar Triangulations II: The Case λ = τ + 1
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DOI: 10.1016/J.DISC.2006.05.039
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description: scientific article; zbMATH DE number 5121350