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Let P(G, λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically euqivalent, denoted G ∼ H, if P(G, λ) = P(H, λ). We write [G] = {H/H ∼ G}. If [G] = {G}, then G is said to be chromatically unique. In this paper, we discuss a chromatically equivalent pair of graphs in one family of K4-homeomorphs, K4(1, 2, 8, d, e, f). The obtained result can be extended in the study of chromatic equivalence classes of K4(1, 2, 8, d, e, f) and chromatic uniqueness of K4-homeomorphs with girth 11.
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Tom
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123--131
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Bibliogr. 18 poz., rys.
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autor
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- Universiti Sains Malaysia School of Mathematical Sciences 11800 Penang, Malaysia, aspa777@gmail.com
Bibliografia
- [1] S. Catada-Ghimire, H. Roslan, Y.H. Peng, On chromatic uniqueness of a family of K4-homeomorphs, Bull. Malays. Math. Sci. Soc. (2) 32 (2009) 3, 327–333.
- [2] S. Catada-Ghimire, H. Roslan, Y.H. Peng, On chromatic equivalence of a family of K4-homeomorphs, Far-East Journal of Mathematical Sciences 30 (2008) 2, 389–400.
- [3] S. Catada-Ghimire, H. Roslan, Y.H. Peng, On chromatic equivalence of K4-homeomorphs II, Advances and Application in Discrete Mathematics 3 (2009) 1, 53–66.
- [4] S. Catada-Ghimire, H. Roslan, Y.H. Peng, On chromatic equivalence of K4-homeomorphs , Southeast Asian Bulletin of Mathematics 33 (2009), 749–757.
- [5] X.E. Chen, K.Z. Ouyang, Chromatic classes of certain 2-connected (n, n + 2)-graphs homeomorphs to K4, Discrete Mathematics 172 (1997), 17–29.
- [6] F.M. Dong, K.M. Koh, K.L. Teo, Chromatic polynomials and chromaticity of graphs, World Scientific Publishing Co. Ptd. Ltd., Singapore, 2005, 118–123.
- [7] K.M. Koh, K.L. Teo, The search for chromatically unique graphs, Graph. Combin. 6 (1990), 259–285.
- [8] W.M. Li, Almost every K4-homeomorphs is chromatically unique, Ars Combin. 23 (1987), 13–36.
- [9] Y.L. Peng, Some new results on chromatic uniqueness of K4-homeomorphs, Discrete Mathematics 288 (2004), 177–183.
- [10] Y.L. Peng, Chromaticity of family of K4-homeomorphs, personal communication (2006).
- [11] Y.L. Peng, Chromatic uniqueness of a family of K4-homeomorphs, Discrete Mathematics 308 (2008), 6132–6140.
- [12] Y.L. Peng, On the chromatic equivalence classes of K4-(1,3,3,δ,ǫ,η), J. Qinghai Normal Univ. 4 (2003), 1–3 [in Chinese].
- [13] Y.L. Peng, Zengyi, On the chromatic equivalence of two families K4-homeomorphs, J. Suzhou Sci. Technol. Univ. 4 (2004), 31–34 [in Chinese].
- [14] Y.L. Peng, Chromatic equivalence of a family of K4-homeomorphs, J. Shanghai Normal Univ. (Natural Sciences) 33 (2004) 4, 9–11 [in Chinese].
- [15] S. Xu, A lemma in studying chromaticity, Ars. Combin. 32 (1991), 315–318.
- [16] C.Y. Chao, L.C. Zhao, Chromatic polynomials of a family of graphs, Ars. Combin. 15 (1983), 111–129.
- [17] E.G. Whitehead Jr., L.C. Zhao, Chromatic uniqueness and equivalence of K4-homeomorphs, Journal of Graph Theory 8 (1984), 355–364.
- [18] W.M. Li, Almost every K4-homeomorphs is chromatically unique, Ars Combin. 23 (1987), 13–36.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-AGHT-0002-0018