一类带号图构形的Tutte多项式

研究了带号曲轮图和带号双半轮图对应图构形的Tutte多项式，主要用带号图的删除-限制定理来计算其Tutte多项式，并运用带号图的符号转换函数找到了几种有规律的基本图形（基图），推导出这些基本图形Tutte多项式的递推公式后，通过计算机辅助给出这类带号图的Tutte多项式，进而得到特征多项式及OS代数的维数。最后计算了半螺旋双吸泵3种不同内部结构的Tutte多项式。

Tutte polynomials of a class of signed graphic arrangements

Tutte polynomials of twisted wheels with a negative edge and double half-wheels with a negative edge have been studied. The Tutte polynomials of signed twisted wheels and signed double half-wheels have been calculated by using the deletion-restriction theorem of signed graphs. By using the transformation function in the deletion-restriction theorem of signed graphs, several regular basic graphs have been found. Recursive formulas of Tutte polynomials for these basic graphs have been derived. Then the Tutte polynomials of this class of signed graphs are obtained with the aid of computation. Furthermore, the characteristic polynomials of the class of signed graphs have been obtained. Finally, the OS algebraic dimension of this class of signed graphic arrangements was obtained. Using the results, the Tutte polynomials of a double suction pump with semi-volutes for three different internal structures were calculated.