$R(G)\ge -1$的图族伴随多项式最小根极值的刻画

On Extremes of Minimum Real Roots of Adjoint Polynomials of Graphs with $R(G)\geq -1$

中文关键词:  伴随多项式  特征标  最小根  序.

英文关键词:adjoint polynomial  character  minimum roots  order.

中文摘要:

      本文引入了图族伴随多项式的最小根极值,用它刻画了特征标不小于$-1$的图族伴随多项式的最小根极值,给出了其对应的极图, 并由此得到了一些有关这些图族伴随多项式最小根序关系的新结果.

英文摘要:

      In this paper, the extremes of the minimum real roots of the adjoint polynomials of graphs are defined, and the graphs with $R(G)\geq -1$ are characterized by the extremes of the minimum real roots of its adjoint polynomials. Moreover, the root extreme graphs of the adjoint polynomials of graphs with $R(G)\geq -1$ are given. Then, some new results on the order of the minimum real roots of the adjoint polynomials of graphs are obtained.