الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The aim of this thesis is to study the polynomial invariants of knots and the polynomial invariants of graph theory and the relation between them in order to use this relation in applications. We have a procedure to study discrete dynamical systems by deriving the knots of the closed periodic orbits of the solution and then we deduce the associated graph and calculate the Tutte polynomial invariant of the graph. We have taken Puu discrete dynamical as an example. (I) We give a mathematical introduction to knot theory and braid theory , this shows that we can convert the topological problem to an algebraic group theory problem. Also an introduction for some knot polynomial invariants are given. (II) We introduce some basic definitions of graph theory. It contains also the polynomial invariant of the graphs, the chromatic, diechromatic and Tutte polynomial invariants. (III) We establish the relation between theory of knots and theory of graphs, this will be done through universes, Jordan trails, shading graphs and Siefert graphs. We show how to find a knot invariants from chromatic and diechromatic polynomial of graphs. (IV) We give the connection between the invariants of graphs and the invariants of knots. It contains also the bracket polynomial, universes and states. (V) We make a realization of our technique. We review a procedure to drive the corresponding knots from the orbit of a discrete dynamical systems and then we use our techniques to derive Tutte polynomial invariant of the graph of the corresponding knot, we deduce also an atlas to explain how to derive such polynomial invariant of the graph of the orbit.