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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| author | Chia G.L. Ho C.-K. |
| author2 | 55914572800 |
| author_facet | 55914572800 Chia G.L. Ho C.-K. |
| author_sort | Chia G.L. |
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| content_provider | Universiti Tenaga Nasional |
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| continent | Asia |
| country | Malaysia |
| 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. |
| format | Article |
| id | my.uniten.dspace-30850 |
| institution | Universiti Tenaga Nasional |
| publishDate | 2023 |
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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 |
| 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 |
| title | 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_short | Chromatic equivalence classes of complete tripartite graphs |
| title_sort | chromatic equivalence classes of complete tripartite graphs |
| 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 |
| url_provider | http://dspace.uniten.edu.my/ |