论文标题
关于统治多项式的非兴趣
On the Unimodality of Domination Polynomials
论文作者
论文摘要
如果多项式的系数不折叠，然后不侵入，则据说是单峰。图$ g $的统治多项式是$ g $中每个基数的支配数量的生成函数，其系数已被猜想为单峰。在本文中，我们将显示路径，循环和完整多部分图的主导地位是单峰的，并且几乎每个图的支配多项式都是单模式的，带有模式$ \ lceil \ lceil \ frac {n} {2} {2} \ rceil $。
A polynomial is said to be unimodal if its coefficients are non-decreasing and then non-increasing. The domination polynomial of a graph $G$ is the generating function of the number of domination sets of each cardinality in $G$, and its coefficients have been conjectured to be unimodal. In this paper we will show the domination polynomial of paths, cycles and complete multipartite graphs are unimodal, and that the domination polynomial of almost every graph is unimodal with mode $ \lceil \frac{n}{2}\rceil $.
