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The aim of this chapter gives more valuable information about many Fractal Graphs. It analyses the structure, implementation of vertices, Edges and angles of two different Fractal Graphs for all Iteration.One is Cantor Set which is one dimensional fractal graph and secondis Hilbert curve which is one of the types of Fractal Antenna and two dimensional Fractal Graph also. It finds out the implementation of Vertices and Edges at all iteration follows the Constant Formulae in the Fractal Graph. This chapter shows that in which formulae is applied for the implementation of vertices and Edges in the Fractal Graph.Matching is one of the very important and more scope topic in Graph Theory. Calculation of Maximal Matching is one of the major evaluations in this chapter. It finds the new formulae separately for calculating cardinality in Matching which is depending on the total number of vertices and total number of edges in the corresponding Iteration of the given Fractal Graph. Calculation of Maximal Matching can be determined by using Iterative Methods and also it can be implemented by Theorem.