How to Burn a Graph

Q3 Mathematics Internet Mathematics Pub Date : 2015-07-23 DOI:10.1080/15427951.2015.1103339
A. Bonato, J. Janssen, Elham Roshanbin
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引用次数: 67

Abstract

ABSTRACT We introduce a new graph parameter called the burning number, inspired by contact processes on graphs such as graph bootstrap percolation, and graph searching paradigms such as Firefighter. The burning number measures the speed of the spread of contagion in a graph; the lower the burning number, the faster the contagion spreads. We provide a number of properties of the burning number, including characterizations and bounds. The burning number is computed for several graph classes, and is derived for the graphs generated by the Iterated Local Transitivity model for social networks.
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如何烧掉图形
摘要:受图上的接触过程(如图自举渗透)和图搜索范式(如消防员)的启发,我们引入了一个新的图参数——燃烧数。燃烧的数字以图表的形式衡量传染病传播的速度;燃烧的数字越低,传染的速度就越快。我们提供了燃烧数的一些性质,包括表征和界。计算了几种图类的燃烧数,并推导了由迭代局部传递模型生成的社交网络图的燃烧数。
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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Internet Mathematics
Internet Mathematics Mathematics-Applied Mathematics
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