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Chromatic equivalence classes of complete tripartite graphs

Some necessary conditions on a graph which has the same chromatic polynomial as the complete tripartite graph Km, n, r are developed. Using these, we obtain the chromatic equivalence classes for Km, n, n (where 1 ? m ? n) and Km1, m2, m3 (where | mi - mj | ? 3). In particular, it is shown that (i) K...

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Main Authors:	Chia G.L., Ho C.-K.
Other Authors:	55914572800
Format:	Article
Published:	2023
Subjects:	Chromatic polynomials Chromatic uniqueness Complete tripartite graphs Equivalence classes Polynomial approximation Polynomials Set theory Complete solutions Graph theory
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id	my.uniten.dspace-30850
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spelling	my.uniten.dspace-308502023-12-29T15:54:37Z Chromatic equivalence classes of complete tripartite graphs Chia G.L. Ho C.-K. 55914572800 7404653303 Chromatic polynomials Chromatic uniqueness Complete tripartite graphs Equivalence classes Polynomial approximation Polynomials Set theory Chromatic polynomials Chromatic uniqueness Complete solutions Complete tripartite graphs Graph theory Some necessary conditions on a graph which has the same chromatic polynomial as the complete tripartite graph Km, n, r are developed. Using these, we obtain the chromatic equivalence classes for Km, n, n (where 1 ? m ? n) and Km1, m2, m3 (where \| mi - mj \| ? 3). In particular, it is shown that (i) Km, n, n (where 2 ? m ? n) and (ii) Km1, m2, m3 (where \| mi - mj \| ? 3, 2 ? mi, i = 1, 2, 3) are uniquely determined by their chromatic polynomials. The result (i), proved earlier by Liu et�al. [R.Y. Liu, H.X. Zhao, C.Y. Ye, A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs, Discrete Math. 289 (2004) 175-179], answers a conjecture (raised in [G.L. Chia, B.H. Goh, K.M. Koh, The chromaticity of some families of complete tripartite graphs (In Honour of Prof. Roberto W. Frucht), Sci. Ser. A (1988) 27-37 (special issue)]) in the affirmative, while result (ii) extends a result of Zou�[H.W. Zou, On the chromatic uniqueness of complete tripartite graphs Kn1, n2, n3 J. Systems Sci. Math. Sci. 20 (2000) 181-186]. � 2008 Elsevier B.V. All rights reserved. Final 2023-12-29T07:54:37Z 2023-12-29T07:54:37Z 2009 Article 10.1016/j.disc.2007.12.059 2-s2.0-56349129702 https://www.scopus.com/inward/record.uri?eid=2-s2.0-56349129702&doi=10.1016%2fj.disc.2007.12.059&partnerID=40&md5=68fe14dd988ed9be62455a294cc9b01c https://irepository.uniten.edu.my/handle/123456789/30850 309 1 134 143 All Open Access; Bronze Open Access Scopus
institution	Universiti Tenaga Nasional
building	UNITEN Library
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continent	Asia
country	Malaysia
content_provider	Universiti Tenaga Nasional
content_source	UNITEN Institutional Repository
url_provider	http://dspace.uniten.edu.my/
topic	Chromatic polynomials Chromatic uniqueness Complete tripartite graphs Equivalence classes Polynomial approximation Polynomials Set theory Chromatic polynomials Chromatic uniqueness Complete solutions Complete tripartite graphs Graph theory
spellingShingle	Chromatic polynomials Chromatic uniqueness Complete tripartite graphs Equivalence classes Polynomial approximation Polynomials Set theory Chromatic polynomials Chromatic uniqueness Complete solutions Complete tripartite graphs Graph theory Chia G.L. Ho C.-K. Chromatic equivalence classes of complete tripartite graphs
description	Some necessary conditions on a graph which has the same chromatic polynomial as the complete tripartite graph Km, n, r are developed. Using these, we obtain the chromatic equivalence classes for Km, n, n (where 1 ? m ? n) and Km1, m2, m3 (where \| mi - mj \| ? 3). In particular, it is shown that (i) Km, n, n (where 2 ? m ? n) and (ii) Km1, m2, m3 (where \| mi - mj \| ? 3, 2 ? mi, i = 1, 2, 3) are uniquely determined by their chromatic polynomials. The result (i), proved earlier by Liu et�al. [R.Y. Liu, H.X. Zhao, C.Y. Ye, A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs, Discrete Math. 289 (2004) 175-179], answers a conjecture (raised in [G.L. Chia, B.H. Goh, K.M. Koh, The chromaticity of some families of complete tripartite graphs (In Honour of Prof. Roberto W. Frucht), Sci. Ser. A (1988) 27-37 (special issue)]) in the affirmative, while result (ii) extends a result of Zou�[H.W. Zou, On the chromatic uniqueness of complete tripartite graphs Kn1, n2, n3 J. Systems Sci. Math. Sci. 20 (2000) 181-186]. � 2008 Elsevier B.V. All rights reserved.
author2	55914572800
author_facet	55914572800 Chia G.L. Ho C.-K.
format	Article
author	Chia G.L. Ho C.-K.
author_sort	Chia G.L.
title	Chromatic equivalence classes of complete tripartite graphs
title_short	Chromatic equivalence classes of complete tripartite graphs
title_full	Chromatic equivalence classes of complete tripartite graphs
title_fullStr	Chromatic equivalence classes of complete tripartite graphs
title_full_unstemmed	Chromatic equivalence classes of complete tripartite graphs
title_sort	chromatic equivalence classes of complete tripartite graphs
publishDate	2023
_version_	1806423385290309632
score	13.222552

Chromatic equivalence classes of complete tripartite graphs

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