On the chromatic uniqueness of the graph \(W(n,n-2)+K_ k\)
type: Item
instance of: scholarly article
title: On the chromatic uniqueness of the graph \(W(n,n-2)+K_ k\)
zbMATH Open document ID: 0837.05055
DOI: 10.1016/0012-365X(94)00056-O
author: Yanpei Liu
author: F. M. Dong
published in: Discrete Mathematics
publication date: 1996-04-23T00:00:00Z
review text: Let \(P(G,\lambda)\) be the chromatic polynomial of a graph \(G\). Two graphs \(G\) and \(H\) are said to be chromatically equivalent if \(P(G, \lambda) = P(H, \lambda)\). A graph \(G\) is chromatically unique if \(G\) is isomorphic to \(H\) for any graph \(H\) such that \(H\) and \(G\) are chromatically equivalent. Let \(W(n,n - 2)\) denote the wheel \(W_n\) with a missing spoke, and \(W(n,n - 2) + K_k\) the join of \(W(n,n - 2)\) and the complete graph \(K_k\) which is obtained from the union of \(W(n,n - 2)\) and \(K_k\). \textit{G. L. Chia} [Discrete Math. 82, No. 2, 209-212 (1990; Zbl 0712.05025)] proved that \(W(n,n-2)\) is chromatically unique for any even \(n \geq 6\). In the present paper the authors generalize this result by showing that the joint graph \(W(n,n - 2) + K_k\) is chromatically unique for any even integer \(n \geq 6\) and integer \(k \geq 0\).
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 810258
zbMATH Keywords: chromatic uniqueness
zbMATH Keywords: chromatic polynomial
zbMATH Keywords: chromatically equivalent
zbMATH Keywords: chromatically unique
zbMATH Keywords: wheel
reviewed by: Marek Kubale
MaRDI profile type: Publication
cites work: Onq-trees
cites work: The chromaticity of wheels with a missing spoke
cites work: The search for chromatically unique graphs
cites work: Chromaticity of two-trees
description: scientific article; zbMATH DE number 810258