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A new family of chromatically unique 6-bridge graph.

  • Karim, N. S. A. [1] ; Hasni, R. [2]
    1. [1] Sultan Idris Education University

      Sultan Idris Education University

      Malasia

    2. [2] University Malaysia Terengganu.
  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 37, Nº. 2, 2018, págs. 239-263
  • Idioma: inglés
  • DOI: 10.4067/s0716-09172018000200239
  • Enlaces
  • Resumen
    • For a graph G, let P(G, λ) denote the chromatic polynomial of G. Two graphs G and H are chromatically equivalent (or simply χ−equivalent), denoted by G ∼ H, if P(G, λ) = P(H, λ). A graph G is chromatically unique (or simply χ−unique) if for any graph H such as H ∼ G, we have H ∼ = G, i.e, H is isomorphic to G. In this paper, the chromatic uniqueness of a new family of 6-bridge graph θ(a, a, b, b, b, c) where 2 ≤ a ≤ b ≤ c, is investigated.

  • Referencias bibliográficas
    • X. W. Bao and X. E. Chen, Chromaticity of the graph θ(a, b, c, d, e) (in Chinese), J. Xinjiang Univ. Natur. Sci. 11, pp. 19-22, (1994).
    • C. Y. Chao and E. G. Whitehead Jr., On chromatic equivalence of graphs, Theory and Applications of Graphs, Lecture Notes in Math. 642, Springer,...
    • X. E. Chen, X. W. Bao and K. Z. Ouyang, Chromaticity of the graph θ(a, b, c, d), J. Shaanxi Normal Univ. 20, pp. 75-79, (1992).
    • F. M. Dong, K. M. Koh and K. L. Teo, Chromatic polynomials and chromaticity of graphs, World Scientific Publishing Ptd. Ltd., Singapore, pp....
    • F. M. Dong, K. L. Teo, C. H. C. Little, M. Hendy and K. M. Koh, Chromatically unique multibridge graphs, The Electric Journal of Combinatorics...
    • F. Harary, Graph theory, Addison-Wesley Publishing Company Inc., United States of America, (1972).
    • N. S. A. Karim, R. Hasni and G.C. Lau, Chromatic uniqueness of 6-bridge graph θ(a, a, a, b, b, c), Electronic Journal of Graph Theory and...
    • N. S. A. Karim, Chromaticity of K4-homeomorphs with girth 9 and 6-bridge graph, Doctoral Dissertation, Universiti Malaysia Terengganu, Terengganu,...
    • A. M. Khalaf, Chromaticity of a certain k-bridge graphs, Doctoral Dissertation, Universiti Putra Malaysia, Serdang, Malaysia, (2010).
    • A. M. Khalaf and Y. H. Peng, Another proof of a family of chromatically unique 5-bridge graphs, International Journal of Applied Mathematics...
    • A. M. Khalaf and Y. H. Peng, A note on chromaticity of k-bridge graphs, Far East J. Math. Sci. 34(3), pp. 353-359, (2009).
    • A. M. Khalaf and Y. H. Peng, The chromatic uniqueness of a family of 6-bridge graphs, AKCE J. Graphs Combin. 6(3), pp. 393-400, (2009).
    • A. M. Khalaf and Y. H. Peng, Chromaticity of the 6-bridge graph θ(a, a, a, b, c, c), International Journal of Applied Mathematics 22(7), pp....
    • A. M. Khalaf and Y. H. Peng, A family of chromatically unique 6-bridge graphs, Ars Combin. 94, pp. 211-220, (2010).
    • A. M. Khalaf, Y. H. Peng and K. A. Atan, Chromaticity of 5-bridge graphs (II), International Journal of Applied Mathematics 23, pp. 791-808,...
    • K. M. Koh and K. L. Teo, The search for chromatically unique graphs, Graphs Combin. 6, pp. 259-285, (1990).
    • K. M. Koh and K. L. Teo, The search for chromatically unique graphs-II, Discrete Math. 172, pp. 59-78, (1997).
    • X. F. Li, A family of chromatically unique 5-bridge graphs, Ars Combin. 88, pp. 415-428, (2008).
    • X. F. Li and X. S. Wei, The chromatic uniqueness of a family of 5-bridge graphs (in Chinese), J. Qinghai Normal Univ. 2, pp. 12-17, (2001).
    • B. Loerinc, Note: Chromatic uniqueness of the generalized θ-graph, Discrete Math. 23, pp. 313-316, (1978).
    • D. B. West, Introduction to graph theory 2nd ed., Prentice Hall, Inc., United States of America, (2001).
    • S. Xu, J. Liu and Y. H. Peng, The chromaticity of s-bridge graphs and related graphs, Discrete Math. 135, pp 349-358, (1994).
    • C. F. Ye, The chromatic uniqueness of 6-bridge graphs (in Chinese), J. Math. Study 34(4), pp. 399-421, (2001).
    • C. F. Ye, The chromatic uniqueness of s-bridge graphs (in Chinese), J. Xinjiang Univ. Natur. Sci. 19(3), pp. 246-265, (2002).

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