完全解决图$\overline{B_{n-8,1,4}}$的色等价类

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

中文关键词:  色等价类  伴随多项式  最小实根  第四不变量.

英文关键词:chromatic equivalence class  adjoint polynomial  the smallest real root  the fourth character.

中文摘要:

      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.

英文摘要:

      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 $B_{n-8,1,4}$.