Geodesic
Graph labelings and continuous factors of dynamical systems
Stephen M. Shea1
1St. Anselm College
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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A labeling of a graph is a function from the vertex set of the graph to some finite set. Certain dynamical systems (such as topological Markov shifts) can be defined by directed graphs. In these instances, a labeling of the graph defines a continuous, shift-commuting factor of the dynamical system. We find sufficient conditions on the labeling to imply classification results for the factor dynamical system. We define the topological entropy of a (directed or undirected) graph and its labelings in a way that is analogous to the definition of topological entropy for a shift space in symbolic dynamics. We show, for example, if $G$ is a perfect graph, all proper $\chi(G)$-colorings of $G$ have the same entropy, where $\chi(G)$ is the chromatic number of $G$.
DOI : 10.37236/2213
Classification : 05C78, 05C15, 37A35, 37B40
Mots-clés : distinguishing labeling, entropy, finitary isomorphism, graph coloring, graph entropy, topological entropy

Stephen M. Shea  1

1 St. Anselm College 
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     title = {Graph labelings and continuous factors of dynamical systems},
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Stephen M. Shea. Graph labelings and continuous factors of dynamical systems. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2213

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