English

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 Z2Z_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.

Keywords

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

R2 v1 2026-06-21T20:01:09.199Z