ENTROPY OF DYNAMICAL SYSTEMS ON WEIGHTS OF A GRAPH

Let G be a nite simple graph whose vertices and edges are weighted by two functions. In this paper we shall de ne and calculate entropy of a dynamical system on weights of the graph G, by using the weights of vertices and edges of G. We examine the conditions under which entropy of the dynamical system is zero, possitive or +∞. At the end it is shown that, for r Є [0,+∞], there exists an order preserving transformation with entropy r.