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Harmonic evolutions on graphs (1201.1355v1)
Published 6 Jan 2012 in math.CO, cs.DM, and math.DS
Abstract: We define the harmonic evolution of states of a graph by iterative application of the harmonic operator (Laplacian over $Z_2$). This provides graphs with a new geometric context and leads to a new tool to analyze them. The digraphs of evolutions are analyzed and classified. This construction can also be viewed as a certain topological generalization of cellular automata.