Original scientific paperThis article has explained in detail what the puzzle of Sudoku isthe meaning of Sudoku -, where it comes fromthe origin of Sudoku and how it can be solvedthe solution way of Sudoku. Especially, this paper has analyzed the solution of the problem -Sudoku can be taken as a problembased on the graph theory. This theory consists of several algorithms, methods, rules and principles which are about the graph in general. In addition, this study has focused on the Welsh-Powell algorithmgreedy coloring algorithm -and Karger's algorithmcontraction algorithmamong those graph algorithms by trying to give explanations about them (these two methods). Also, based on the rules and principles of those two algorithms, "Sudoku Solver Application" has been designed and developed in order to solve the puzzle of Sudoku. Moreover, the paper has presented a specific solution way of the puzzle Sudoku, and has showed its efficiency and usability by showing complexity and run time of the application among several available solutions based on the graph theory. So, the study has offered "Sudoku Solver Application" to the game world, science world, and education world as well for its use.