燃烧杠铃的数量

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-03-27 DOI:10.1007/s10255-024-1113-8

Hui-qing Liu, Rui-ting Zhang, Xiao-lan Hu

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引用次数: 0

摘要

图 G 的燃烧数 b(G)定义为：对于图 G 的每个顶点 u，存在 i∈ {1,...,k}，且 dG(u,xi)≤k-i，以及 dG(xi,xj)≥j-i（对于任意 1≤i <j≤k）的最小整数 k，对于该整数，存在顶点 x1,...,xk，且对于图 G 的每个顶点 u，存在 i∈ {1,...,k}，且 dG(u,xi)≤k-i。即使对于某些最大阶数为三的无循环图，图燃烧问题也被证明是 NP-完全的。在本文中，我们将分别确定所有短杠铃和长杠铃的燃烧数。

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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Burning Numbers of Barbells

Motivated by a discrete-time process intended to measure the speed of the spread of contagion in a graph, the burning number b(G) of a graph G, is defined as the smallest integer k for which there are vertices x₁,…,x_k such that for every vertex u of G, there exists i ∈ {1,…,k} with d_G(u, x_i) ≤ k − i, and d_G(x_i, x_j) ≥ j − i for any 1 ≤ i < j ≤ k. The graph burning problem has been shown to be NP-complete even for some acyclic graphs with maximum degree three. In this paper, we determine the burning numbers of all short barbells and long barbells, respectively.

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来源期刊

Acta Mathematicae Applicatae Sinica, English Series 数学-应用数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.