Discussiones Mathematicae Graph Theory 28(2) (2008)
189-218
doi: 10.7151/dmgt.1401
Jianfeng Wang^{1,2}, Qiongxiang Huang^{2}, Chengfu Ye^{1} and Ruying Liu^{1}
^{1}Department of Mathematics and Information Science
Qinghai Normal University, Xining, Qinghai 810008, P.R. China
^{2}College of Mathematics and System Science
Xinjiang University, Urumqi, Xinjiang 830046, P.R. China
e-mail: jfwang4@yahoo.com.cn
Keywords: chromatic equivalence class, adjoint polynomial, the smallest real root, the second smallest real root, the fourth character.
2000 Mathematics Subject Classification: 05C15, 05C60.
[1] | J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (North-Holland, Amsterdam, 1976). |
[2] | F.M. Dong, K.M. Koh, K.L. Teo, C.H.C. Little and M.D. Hendy, Two invariants for adjointly equivalent graphs, Australasian J. Combin. 25 (2002) 133-143. |
[3] | F.M. Dong, K.L. Teo, C.H.C. Little and M.D. Hendy, Chromaticity of some families of dense graphs, Discrete Math. 258 (2002) 303-321, doi: 10.1016/S0012-365X(02)00355-2. |
[4] | Q.Y. Du, The graph parameter π(G) and the classification of graphs according to it, Acta Sci. Natur. Univ. Neimonggol 26 (1995) 258-262. |
[5] | B.F. Huo, Relations between three parameters A(G), R(G) and D_{2}(G) of graph G (in Chinese), J. Qinghai Normal Univ. (Natur. Sci.) 2 (1998) 1-6. |
[6] | K.M. Koh and K.L. Teo, The search for chromatically unique graphs, Graphs and Combin. 6 (1990) 259-285, doi: 10.1007/BF01787578. |
[7] | K.M. Koh and K.L. Teo, The search for chromatically unique graphs-II, Discrete Math. 172 (1997) 59-78, doi: 10.1016/S0012-365X(96)00269-5. |
[8] | R.Y. Liu, Several results on adjoint polynomials of graphs (in Chinese), J. Qinghai Normal Univ. (Natur. Sci.) 1 (1992) 1-6. |
[9] | R.Y. Liu, On the irreducible graph (in Chinese), J. Qinghai Normal Univ. (Natur. Sci.) 4 (1993) 29-33. |
[10] | R.Y. Liu and L.C. Zhao, A new method for proving uniqueness of graphs, Discrete Math. 171 (1997) 169-177, doi: 10.1016/S0012-365X(96)00078-7. |
[11] | R.Y. Liu, Adjoint polynomials and chromatically unique graphs, Discrete Math. 172 (1997) 85-92, doi: 10.1016/S0012-365X(96)00271-3. |
[12] | J.S. Mao, Adjoint uniqueness of two kinds of trees (in Chinese), The thesis for Master Degree (Qinghai Normal University, 2004). |
[13] | R.C. Read and W.T. Tutte, Chromatic Polynomials, in: L.W. Beineke, R.T. Wilson (Eds), Selected Topics in Graph Theory III (Academiv Press, New York, 1988) 15-42. |
[14] | S.Z. Ren, On the fourth coefficients of adjoint polynomials of some graphs (in Chinese), Pure and Applied Math. 19 (2003) 213-218. |
[15] | J.F. Wang, R.Y. Liu, C.F. Ye and Q.X. Huang, A complete solution to the chromatic equivalence class of graph `(B_{n−7,1,3}), Discrete Math. 308 (2008) 3607-3623. |
[16] | C.F. Ye, The roots of adjoint polynomials of the graphs containing triangles, Chin. Quart. J. Math. 19 (2004) 280-285. |
[17] | H.X. Zhao, Chromaticity and Adjoint Polynomials of Graphs, The thesis for Doctor Degree (University of Twente, 2005). The Netherlands, Wöhrmann Print Service (available at http://purl.org/utwente/50795). |
Received 30 November 2006
Revised 26 February 2008
Accepted 28 February 2008