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Chromatic equivalence classes of complete tripartite graphs

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dc.citedby12
dc.contributor.authorChia G.L.en_US
dc.contributor.authorHo C.-K.en_US
dc.contributor.authorid55914572800en_US
dc.contributor.authorid7404653303en_US
dc.date.accessioned2023-12-29T07:54:37Z
dc.date.available2023-12-29T07:54:37Z
dc.date.issued2009
dc.description.abstractSome 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.en_US
dc.description.natureFinalen_US
dc.identifier.doi10.1016/j.disc.2007.12.059
dc.identifier.epage143
dc.identifier.issue1
dc.identifier.scopus2-s2.0-56349129702
dc.identifier.spage134
dc.identifier.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-56349129702&doi=10.1016%2fj.disc.2007.12.059&partnerID=40&md5=68fe14dd988ed9be62455a294cc9b01c
dc.identifier.urihttps://irepository.uniten.edu.my/handle/123456789/30850
dc.identifier.volume309
dc.pagecount9
dc.relation.ispartofAll Open Access; Bronze Open Access
dc.sourceScopus
dc.sourcetitleDiscrete Mathematics
dc.subjectChromatic polynomials
dc.subjectChromatic uniqueness
dc.subjectComplete tripartite graphs
dc.subjectEquivalence classes
dc.subjectPolynomial approximation
dc.subjectPolynomials
dc.subjectSet theory
dc.subjectChromatic polynomials
dc.subjectChromatic uniqueness
dc.subjectComplete solutions
dc.subjectComplete tripartite graphs
dc.subjectGraph theory
dc.titleChromatic equivalence classes of complete tripartite graphsen_US
dc.typeArticleen_US
dspace.entity.typePublication
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