How to Burn a Graph. Issue 1 (3rd March 2016)

• Record Type: Journal Article
• Authors: Bonato, Anthony; Janssen, Jeannette; Roshanbin, Elham
• Is Part Of: Internet mathematics. Volume 12:Issue 1/2(2016)
• Page Start: 85
• Page End: 100
• Publication Date: 2016-03-03
• Subjects: Internet -- Mathematics -- Periodicals; Information networks -- Mathematics -- Periodicals; Information networks; Internet; Periodicals; 004.0151
• DOI: 10.1080/15427951.2015.1103339
• Languages: English
• ISSNs: 1944-9488

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 .