Abstract
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 of a graph is the minimum number of steps in a graph burning process for that graph. In this paper, we consider the burning number of graph products. We find some general bounds on the burning number of the Cartesian product and the strong product of graphs. In particular, we determine the asymptotic value of the burning number of hypercube graphs and we present a conjecture for its exact value. We also find the asymptotic value of the burning number of the strong grids, and using that we obtain a lower bound on the burning number of the strong product of graphs in terms of their diameters. Finally, we consider the burning number of the lexicographic product of graphs and we find a characterization for that.
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