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| Abstract : |
| For a graph G, suppose P(G,l) be the chromatic polynomial of G. Two graphs G and H are said to be chromatically equivalent (or simply χ-equivalent), denoted by G ~ H, if P(G, λ)= P(H, λ). A graph G is said to be chromatically unique (or simply χ-unique) if for any graph H such that H ~ G, we have H ≅ G, i.e. H is isomorphic to G. In this paper, the chromatic uniqueness of a family of 6-bridge graphs, that is the graph of the form θ(3,3,b,c,c,c) is determined. |
| References |
1. Chao, C.Y., Whitehead, E.G. On Chromatic Equivalence of Graphs (1978) Theory and Applications of Graphs, pp. 121-131. Cited 69 times.Lecture Notes in Math., edited by Y. Alavi and D. R. Lick (Springer-Verlag, Berlin) 2. Loerinc, B. Chromatic uniqueness of the generalized θ-graph (Open Access)(1978) Discrete Mathematics, 23 (3), pp. 313-316. Cited 33 times. doi: 10.1016/0012-365X(78)90012-2 3. Chen, X.E., Bao, X.W., Ouyang, K.Z. (1992) J. Shaanxi Normal Univ., 20, pp. 75-79. Cited 16 times. 4. Xu, S., Liu, J., Peng, Y. The chromaticity of s-bridge graphs and related graphs (Open Access) (1994) Discrete Mathematics, 135 (1-3), pp. 349-358. Cited 18 times. doi: 10.1016/0012-365X(93)E0091-H 5. Bao, X.W., Chen, X.E. (1994) J. Xinjiang Univ. Natur. Sci., 11, pp. 19-22. Cited 11 times. 6. Li, X.F., Wei, X.S. (2001) J. Qinghai Normal Univ., 2, pp. 12-17. Cited 11 times. (in Chinese). 7. Li, X.-F. A family of chromatically unique 5-bridge graphs (2008) Ars Combinatoria, 88, pp. 415-428. Cited 7 times. 8. Khalaf, A.M. (2010) Chromaticity of Certain K-bridge Graphs. Cited 6 times. Ph.D. thesis, Universiti Putra Malaysia. 9. Khalaf, A.M., Peng, Y.H. (2009) International Journal of Applied Mathematics, 22 (6), pp. 1009-1020. Cited 6 times. 10. Khalaf, A.M., Peng, Y.H., Atan, K.A. (2010) International Journal of Applied Mathematics, 23, pp. 791-808. Cited 7 times. 11. Ye, C.F. (2001) J. Math. Study, 34 (4), pp. 399-421. Cited 6 times. (in Chinese). 12. Khalaf, A.M., Peng, Y.H. (2009) AKCE Journal of Graphs and Combinatorics, 6 (3), pp. 393-400. Cited 7 times. 13. Khalaf, A.M., Peng, Y.H. (2009) International Journal of Applied Mathematics, 22 (7), pp. 1087-1111. Cited 7 times. 14. Khalaf, A.M., Peng, Y.H. A family of chromatically unique 6-bridge graphs (2010) Ars Combinatoria, 94, pp. 211-220. Cited 8 times. 15. Karim, N.S.A., Hasni, R. Chromaticity of 6-bridge graph θ (3,3,3, b, c, d) (2015) AIP Conference Proceedings, 1682, art. no. 040010. http://scitation.aip.org/content/aip/proceeding/aipcp ISBN: 978-073541329-0 doi: 10.1063/1.4932483 16. Abd Karim, N.S., Hasni, R. Chromaticity of 6-bridge Graph θ(3, 3, b, b, c, c) (2016) Malaysian Journal of Mathematical Sciences, 10, pp. 155-166. Cited 2 times. http://einspem.upm.edu.my/journal/list.html 17. Karim, N.S.A., Hasni, R., Lau, G.-C. Chromatically unique 6-bridge graph θ(a, a, a, b, b, c) (Open Access)(2016) Electronic Journal of Graph Theory and Applications, 4 (1), pp. 60-78. Cited 3 times. http://ejgta.org/index.php/ejgta/article/download/149 /pdf_16 doi: 10.5614/ejgta.2016.4.1.6 18. Dong, F.M., Teo, K.L., Little, C.H.C., Hendy, M.D., Koh, K.M. (2004) Electronic Journals of Combin. Theory, 11, p. R12. Cited 3 times. 19. Dong, F.M., Koh, K.M., Teo, K.L. Chromatic polynomials and chromaticity of graphs (2005) Chromatic Polynomials and Chromaticity of Graphs, pp. 1-357. Cited 128 times. http://www.worldscientific.com/worldscibooks/10.1142/5814#t=toc ISBN: 978-981256946-2; 978-981256317-0 doi: 10.1142/5814 20. Koh, K.M., Teo, K.L. The search for chromatically unique graphs (1990) Graphs and Combinatorics, 6 (3), pp. 259-285. Cited 129 times. doi: 10.1007/BF01787578 |
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