Two classes of chromatically unique graphs
type: Item
instance of: scholarly article
title: Two classes of chromatically unique graphs
zbMATH Open document ID: 0697.05027
DOI: 10.1016/0012-365X(90)90041-F
author: B. H. Goh
author: K. M. Koh
published in: Discrete Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The chromatic polynomial of a graph G is denoted by P(G;\(\lambda)\). Then G is said to be chromatically unique if: whenever \(P(H;\lambda)=P(G;\lambda)\), then the graph H is isomorphic to G. In this paper, two new classes of chromatically unique graphs are presented. One of these is obtained from disjoint \(K_ r\) (r\(\geq 3)\) and \(C_ s\) (s\(\geq 3)\) by identifying \(e_ 1\in E(K_ r)\) with \(e_ 2\in C_ s\). The other is obtained, for \(n\geq r+1\geq 5\) (with two exceptions corresponding to \((n,r)=(6,4)\) and (7,4)), from disjoint \(K_ r\) and a graph X of order n which is a \(K_ 4\) homeomorph, by identifying \(K_ 3\) in \(K_ r\) with \(K^ 1_ 3\) in X.
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 4142065
zbMATH Keywords: chromatic polynomial
zbMATH Keywords: chromatically unique graphs
reviewed by: Arthur T. White
MaRDI profile type: Publication
cites work: Chromatic polynomials and whitney's broken circuits
cites work: Chromatic Polynomials
cites work: Q5422499
cites work: On maximally saturated graphs
cites work: On chromatic equivalence of graphs
cites work: Chromatically unique graphs
cites work: Q3313882
cites work: A note on chromatic uniqueness of graphs
cites work: Q3824333
cites work: On chromatic coefficients
cites work: Q3682504
cites work: Q3901538
cites work: Chromatic uniqueness of the generalized \(\Theta\)-graph
cites work: An introduction to chromatic polynomials
cites work: Q3832608
cites work: On the chromatic uniqueness of bipartite graphs
cites work: Cutpoints and the chromatic polynomial
cites work: Chromatic uniqueness and equivalence ofK4 homeomorphs
cites work: The chromaticity of wheels
full work available at URL: 0012-365x(90)90041-f
OpenAlex ID: W2018504413
description: scientific article; zbMATH DE number 4142065