On trees of polygons
type: Item
instance of: scholarly article
title: On trees of polygons
zbMATH Open document ID: 0575.05027
DOI: 10.1007/BF01270490
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: The set S of n-gon-trees is defined recursively as follows: (a) The n-gon is in S. (b) If G is in S, then so is any graph formed by identifying an edge of G with an edge of an n-gon. The authors prove that a graph is an n-gon-tree on k n-gons if and only if its chromatic polynomial is \[ [(\lambda -1)^ n+(-1)^ n(\lambda -1)]^ k/[\lambda (\lambda - 1)]^{k-1}. \] [Reviewer's comments: The elaborate definition of \(Q(C_ n,\lambda)\) in Lemma 5 is unnecessary. Corollary 1.1 is a result due to \textit{G. H. J. Meredith} [J. Comb. Theory, Ser. B 13, 14-17 (1972; Zbl 0218.05056)].]
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 3918392
zbMATH Keywords: n-gon-trees
zbMATH Keywords: chromatic polynomial
author: Chong-Yun Chao
author: Nian Zu Li
reviewed by: Ronald C. Read
MaRDI profile type: Publication
cites work: Chromatic polynomials of connected graphs
cites work: On chromatic coefficients
cites work: An introduction to chromatic polynomials
full work available at URL: https://doi.org/10.1007/bf01270490
OpenAlex ID: W2023472511
description: scientific article; zbMATH DE number 3918392