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Type :article
Subject :Q Science (General)
ISSN :0094243X
Main Author :Nor Suriya Abd Karim
Additional Authors :Roslan Hasni
Title :Chromatic uniqueness of 6-bridge graph θ (3,3, b, c, c, c)
Year of Publication :2017

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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