Abstract
We study the dynamical behavior of functions on vertices of a graph that are contractions in the graph metric. We show that the fixed point set of such functions must be convex. If a function has no fixed points and the graph is a tree, we prove that every dynamical cycle must have an even period and the function behaves eventually like a symmetry.
Citation
Olena Ostapyuk. Mark Ronnenberg. "Discrete dynamics of contractions on graphs." Involve 10 (3) 495 - 503, 2017. https://doi.org/10.2140/involve.2017.10.495
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