Harmonic evolutions on graphs
Combinatorics
2012-01-09 v1 Discrete Mathematics
Dynamical Systems
Abstract
We define the harmonic evolution of states of a graph by iterative application of the harmonic operator (Laplacian over ). 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.
Cite
@article{arxiv.1201.1355,
title = {Harmonic evolutions on graphs},
author = {Jerzy Kocik},
journal= {arXiv preprint arXiv:1201.1355},
year = {2012}
}
Comments
16 pages, 7 figures