Game of Life on Graphs

We consider a specific graph dynamical system inspired by the famous Conway's Game of Life in this work. We study the properties of the dynamical system on different graphs and introduce a new efficient heuristic for graph isomorphism testing. We use the evolution of our system to extract features from a graph in a deterministic way and observe that the extracted features are unique and the distance induced by that features satisfy triangle inequality for all connected graphs with up to ten vertices.