西尔皮斯基图和数据中心网络的生成树数量

IF 0.8 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Information and Computation Pub Date : 2024-07-17 DOI:10.1016/j.ic.2024.105194

Xiaojuan Zhang , Gang Yang , Changxiang He , Ralf Klasing , Yaping Mao

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引用次数: 0

摘要

生成树的数量是一个重要的图不变式，它与图的不同拓扑和动态特性有关，如图的可靠性、同步能力和扩散特性。2007 年，Chang 等人提出了关于 Sierpiński 三角形图的生成树数及其生成树熵的两个猜想。在本文中，我们完全证实了这些猜想。对于数据中心网络 Dk,n，我们得到了 k=1 的精确公式和 k≥2 的上下限。我们的结果还允许计算 Sierpiński 图和数据中心网络的生成树熵。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The number of spanning trees for Sierpiński graphs and data center networks

The number of spanning trees is an important graph invariant related to different topological and dynamic properties of the graph, such as its reliability, synchronization capability and diffusion properties. In 2007, Chang et al. proposed two conjectures on the number of spanning trees of Sierpiński triangle graphs and its spanning tree entropy. In this paper, we completely confirm these conjectures. For data center networks $D_{k, n}$ , we get the exact formula for $k = 1$ , and upper and lower bounds for $k \geq 2$ . Our results allow also the calculation of the spanning tree entropy of Sierpiński graphs and data center networks.

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来源期刊

Information and Computation 工程技术-计算机：理论方法

CiteScore

2.30

自引率

0.00%

发文量

119

审稿时长

140 days

期刊介绍： Information and Computation welcomes original papers in all areas of theoretical computer science and computational applications of information theory. Survey articles of exceptional quality will also be considered. Particularly welcome are papers contributing new results in active theoretical areas such as -Biological computation and computational biology- Computational complexity- Computer theorem-proving- Concurrency and distributed process theory- Cryptographic theory- Data base theory- Decision problems in logic- Design and analysis of algorithms- Discrete optimization and mathematical programming- Inductive inference and learning theory- Logic & constraint programming- Program verification & model checking- Probabilistic & Quantum computation- Semantics of programming languages- Symbolic computation, lambda calculus, and rewriting systems- Types and typechecking