支配多项式为单峰的一些图族

Saeid Alikhani; Somayeh Jahari

支配多项式为单峰的一些图族

组合数学 2014-01-10 v2

作者: Saeid Alikhani , Somayeh Jahari

摘要

设 $G$ 为 $n$ 阶简单图。 $G$ 的支配多项式定义为 $D(G, x)=\sum_{i=\gamma(G)}^{n} d(G,i) x^{i}$ ，其中 $d(G,i)$ 是 $G$ 中大小为 $i$ 的支配集的数量， $\gamma(G)$ 是 $G$ 的支配数。有猜想认为任何图的支配多项式都是单峰的。本文给出了若干支配多项式为单峰的图族。

关键词

支配多项式单峰简单图支配集支配数图族

引用

@article{arxiv.1401.1159,
  title  = {Some families of graphs whose domination polynomials are unimodal},
  author = {Saeid Alikhani and Somayeh Jahari},
  journal= {arXiv preprint arXiv:1401.1159},
  year   = {2014}
}

备注

This paper has been withdrawn by the author due to the following error. I regret to announce that Theorem 3 of that paper is incorrect as stated. The product of two symmetric and unimodal polynomials is symmetric and unimodal. It is not true that the product of two unimodal polynomials is unimodal

支配多项式为单峰的一些图族

摘要

关键词

引用

备注

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