Maximum Matching in Koch Snowflake and Sierpinski Triangle

The goal of this paper presents the method of finding the maximum matching cardinality in the fractal graph. A fractal is uneven or irregular sets of well defined structure that has to be broken up into small pieces, the property of having each piece analogous or identical to the overall structure at random ranges. Fractal graph is an excellent construction of well-defined objects. It provides a general frame work-study of regular self-similarity sets and natural phenomena of the fractal graphs. Matching is the collection of non-touching edges in the graph. Maximum matching is
the largest possible collection of non-touching edges in the graph. This paper is used to determine the constant ratio of maximum matching cardinality in all the iteration of self-similarity Fractal Graph. This paper is used to find the constant ratio between the number of edges in each iteration of the Fractal Graph and the Maximum Cardinality number of Maximum Matching. This provides general formulae for all the
iteration of Koch snowflake and Sierpinski triangle. By using mathematical induction method, it finds the maximum matching constitutive number in all the iterations
of them.