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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     title = {The chromatic equivalence class of graph $\overline{B_{n-6,1,2}}$},
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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/