UPSI Digital Repository (UDRep)
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| For such a graph G, suppose P(G, λ) denote the chromatic polynomial of graph G. Let G and H are two graphs, then 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 G H , we have G H≅ , that is G is isomorphic to H. In this paper, the chromaticity of a family of 6-bridge graph, that is θ (,,,,,) aabbcc is investigated. The result is presented in Theorem 3.1 in Section 3 of this paper. |
| References |
[1] Harary F 1972 Graph Theory (USA: Addison-Wesley Publishing Company Inc.)
[2] West D B 2001 Introduction to Graph Theory (USA: Prentice Hall Inc.)
[3] Dong F M, Koh K M and Teo K L 2005 Chromatic Polynomials and Chromaticity of Graphs (Singapore: World Scientific Publishing Co. Lte. Ptd)
[4] Koh K M and Teo K L 1997 Discrete Mathematics 172 pp 59-78
[5] Chao C Y and Whitehead E G 1978 Theory and Applications of Graphs, Lecture Notes in Math.642 pp 121-131
[6] Loerinc B 1978 Discrete Mathematics 23 pp 313-316
[7] Chen X E, Bao X W and Ouyang K Z 1992 J. Shaanxi Normal Univ. 20 pp 75-79
[8] Xu S J, Liu J J and Peng Y H 1994 Discrete Mathematics 135 pp 349-358
[9] Bao X W and Chen X E 1994 J. Xinjiang Univ. Natur. Sci. 11 pp 19-22
[10] Li X F and Wei X S 2001 J. Qinghai Normal Univ. 2 pp 12-17
[11] Li X F 2008 Combinatoria 88 pp 415-428
[12] Khalaf A M and Peng Y H 2009 International Journal of Applied Mathematics 22(6) pp 1006-1020
[13] Khalaf A M, Peng Y H and Atan K A 2010 International Journal of Applied Mathematics 23 pp 791-808
[14] Ye C F 2001 J. Math. Study 34(4) pp 399-421
[15] Khalaf A M and Peng Y H 2010 Ars Combinatoria 94 pp 211-220
[16] Khalaf A M and Peng 2009 AKCE International Journal of Graphs and Combinatorics 6(3) pp 393-400
[17] Karim N S A and Hasni R 2016 Malaysian Journal of Mathematical Sciences 10(S) pp 155-166
[18] Karim N S A and Hasni R 2014 AIP Conference Proceedings 1635 pp 440-446
[19] Khalaf A M 2010 Chromaticity of certain k-bridge graphs Doctoral Dissertation (Universiti Putra
Malaysia, Serdang, Malaysia)
[20] Khalaf A M and Peng Y H 2009 International Journal of Applied Mathematics 22(7) pp 1087-1111
[21] Karim N S A, Hasni R and Lau G C 2014 Electronic Journal of Graph Theory and Applications
4(1) pp 60-78
[22] Dong F M, Teo, K L, Little C H C, Hendy M D and Koh K M 2004 Electronic Journals of Combinatorics Theory 11 #R12
[23] Koh K M and Teo K L 1990 Graphs and Combinatorics 6(3) pp 349-358 |
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