当前位置:
X-MOL 学术
›
Appl. Math. Comput.
›
论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The number of connected sets in Apollonian networks
Applied Mathematics and Computation ( IF 3.5 ) Pub Date : 2024-06-13 , DOI: 10.1016/j.amc.2024.128883 Zuwen Luo , Kexiang Xu
Applied Mathematics and Computation ( IF 3.5 ) Pub Date : 2024-06-13 , DOI: 10.1016/j.amc.2024.128883 Zuwen Luo , Kexiang Xu
A vertex subset in a graph that induces a connected subgraph is referred to as a connected set. Counting the number of connected sets in a graph is generally a #P-complete problem. In our recent work [Graphs Combin. (2024)], a linear recursive algorithm was designed to count in any Apollonian network. In this paper we extend our research by establishing a tight upper bound on in Apollonian networks with an order of , along with a characterization of the graphs that reach this upper bound. Our approach primarily utilizes linear programming techniques. Moreover, we propose a conjecture regarding the lower bound on in Apollonian networks with a given order.
中文翻译:
阿波罗网络中连通集的数量
图中导出连通子图的顶点子集称为连通集。计算图中连通集的数量通常是一个#P完全问题。在我们最近的工作中[Graphs Combin。 (2024)],线性递归算法被设计用于在任何阿波罗网络中计数。在本文中,我们通过在阿波罗网络中建立一个严格的上限(阶数为 )以及达到该上限的图的特征来扩展我们的研究。我们的方法主要利用线性规划技术。此外,我们提出了关于给定阶数的阿波罗网络下界的猜想。
更新日期:2024-06-13
中文翻译:
![](https://scdn.x-mol.com/jcss/images/paperTranslation.png)
阿波罗网络中连通集的数量
图中导出连通子图的顶点子集称为连通集。计算图中连通集的数量通常是一个#P完全问题。在我们最近的工作中[Graphs Combin。 (2024)],线性递归算法被设计用于在任何阿波罗网络中计数。在本文中,我们通过在阿波罗网络中建立一个严格的上限(阶数为 )以及达到该上限的图的特征来扩展我们的研究。我们的方法主要利用线性规划技术。此外,我们提出了关于给定阶数的阿波罗网络下界的猜想。