The generalized burning number of graphs

摘要

Graph burning is a deterministic discrete time graph process that can be interpreted as a model for the spread of influence in social networks. The burning number b(G) of a graph G is the minimum number of steps in a graph burning process for that graph. In this paper, we introduced a new graph parameter, the generalized burning number of a graph br(G), which is generalization of b(G) with b1(G)=b(G). And then determined the generalized burning number of several graphs and operation graphs. The general bounds on this parameter are also discussed.