A geometrical hierarchy on graphs via cellular automata

Authors:
Bruno Martin
Affiliations:
e-lab, Bouygues SA 1 av Eugene Freyssinet 78061, Saint-Quentin en Yvelines, France
Venue:
Fundamenta Informaticae - Special issue on cellular automata
Year:
2002

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Abstract

Historically, cellular automata were defined on the lattices Zn, but the definition can be extended to bounded degree graphs. Given a notion of simulation between cellular automata defined on different structures (namely graphs of automata), we can deduce an order on graphs. In this paper, we link this order to graph properties and explicit the order for most of the common graphs.