Geodesic
The chromatic equivalence class of graph $\overline{B_{n-6,1,2}}$
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 2, pp. 189-218.

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By h(G,x) and P(G,λ) we denote the adjoint polynomial and the chromatic polynomial of graph G, respectively. A new invariant of graph G, which is the fourth character R₄(G), is given in this paper. Using the properties of the adjoint polynomials, the adjoint equivalence class of graph B_n-6,1,2 is determined, which can be regarded as the continuance of the paper written by Wang et al. [J. Wang, R. Liu, C. Ye and Q. Huang, A complete solution to the chromatic equivalence class of graph B_n-7,1,3, Discrete Math. (2007), doi: 10.1016/j.disc.2007.07.030]. According to the relations between h(G,x) and P(G,λ), we also simultaneously determine the chromatic equivalence class of B_n-6,1,2 that is the complement of B_n-6,1,2.
Keywords: chromatic equivalence class, adjoint polynomial, the smallest real root, the second smallest real root, the fourth character 
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Wang, Jianfeng; Huang, Qiongxiang; Ye, Chengfu; Liu, Ruying. The chromatic equivalence class of graph $\overline{B_{n-6,1,2}}$. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 2, pp. 189-218. http://geodesic.mathdoc.fr/item/DMGT_2008_28_2_a0/

[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 D₂(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 $\overline{B_{n-7,1,3}}$, 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)