Characterization of Q graph by the burning number

Abstract

The burning number $ b(G) $ of a graph $ G $, introduced by Bonato, is the minimum number of steps to burn the graph, which is a model for the spread of influence in social networks. In 2016, Bonato et al. studied the burning number of paths and cycles, and based on these results, they proposed a conjecture on the upper bound for the burning number. In this paper, we determine the exact value of the burning number of $ Q $ graphs and confirm this conjecture for $ Q $ graph. Following this, we characterize the single tail and double tails $ Q $ graph in term of their burning number, respectively.

Keywords

• burning number
• single tail $ q $ graph
• double tails $ q $ graph