A Complete Solution to the Chromatic Equivalence Class of Graph $\overline{B_{n-8,1,4}}$

DOI：10.3770/j.issn:2095-2651.2012.03.001

 作者 单位 毛亚平 青海师范大学数学系, 青海 西宁 810008 冶成福 青海师范大学数学系, 青海 西宁 810008 张淑敏 青海师范大学数学系, 青海 西宁 810008

两个图伴随等价当且仅当它们的补图色等价。利用伴随多项式的性质和第四不变量$R_4(G)$,我们决定出图$B_{n-8,1,4}$的伴随等价类.根据伴随多项式和色多项式的关系,我们自然也就得到了图$B_{n-8,1,4}$的补图$\overline{B_{n-8,1,4}}$的色等价类.

Two graphs are defined to be adjointly equivalent if and only if their complements are chromatically equivalent. Using the properties of the adjoint polynomials and the fourth character $R_4(G)$, the adjoint equivalence class of graph $B_{n-8,1,4}$ is determined. According to the relations between adjoint polynomial and chromatic polynomial, we also simultaneously determine the chromatic equivalence class of $\overline{B_{n-8,1,4}}$ that is the complement of $B_{n-8,1,4}$.