Harmonic evolutions on graphs

Details Harmonic evolutions on graphs Harmonic evolutions on graphs

2012-01-06

arxiv.org/abs/1201.1355v1

International Journal of Mathematics and Computer Science, vol 2 no. 1 (2007), 65-82

Mathematics

Combinatorics

16 pages, 7 figures

Scientific paper

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.

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