الفهرس 
Chapter (1) Introduction and literature reviewOnly 14 pages are availabe for public view
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Abstract
The main objective of this thesis is to make a linkage between graph
theory and ordinary differential equations with first order, first degree such
as (Linear and Bernoulli’s) using simple techniques. Firstly, we transform an
orthogonal double covers graphs (briefly, ODCs) to metric graph which we
can represent it as matrices. Then, we use these matrices to study the relation
between differential equations and the graph theory subject. We use the
generalized Fibonacci polynomials (GFP) and the generalized LUCAS
polynomials (GLP) to transform the differential equations into a system of
equations with undetermined constants. As a conclusion, we solve some
numerical examples and evaluate the errors which prove the efficiency and
accuracy of the method, we use.