共查询到10条相似文献,搜索用时 218 毫秒
1.
2.
Ferenc Bencs 《Discrete Mathematics》2018,341(12):3321-3330
The independence polynomial of a graph is where denotes the number of independent sets of of size (note that ). In this paper we show a new method to prove real-rootedness of the independence polynomials of certain families of trees.In particular we will give a new proof of the real-rootedness of the independence polynomials of centipedes (Zhu’s theorem), caterpillars (Wang and Zhu’s theorem), and we will prove a conjecture of Galvin and Hilyard about the real-rootedness of the independence polynomial of the so-called Fibonacci trees. 相似文献
3.
The Wiener polynomial of a connected graph is defined as , where denotes the distance between and , and the sum is taken over all unordered pairs of distinct vertices of . We examine the nature and location of the roots of Wiener polynomials of graphs, and in particular trees. We show that while the maximum modulus among all roots of Wiener polynomials of graphs of order is , the maximum modulus among all roots of Wiener polynomials of trees of order grows linearly in . We prove that the closure of the collection of real roots of Wiener polynomials of all graphs is precisely , while in the case of trees, it contains . Finally, we demonstrate that the imaginary parts and (positive) real parts of roots of Wiener polynomials can be arbitrarily large. 相似文献
4.
5.
6.
Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, two conjectures on permutation polynomials proposed recently by Wu and Li [19] are settled. Moreover, a new class of permutation trinomials of the form is also presented, which generalizes two examples of [10]. 相似文献
7.
8.
9.
In this paper, we present several necessary conditions for the reversed Dickson polynomial of the second kind to be a permutation of . In particular, we give explicit evaluation of the sum . 相似文献