MUSLIMAH, Umi (2023) Representassi Penyelesaian Masalah Permainan Sudoku Hijaiyah Ukuran 12×12 dalam Pewarnaan Graf. Skripsi thesis, Universitas Jenderal Soedirman.

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Abstract

Sudoku is a logic puzzle game based on combining the placement of numbers in a puzzle. This game has an important role in the development of the brain, emotional, concentration and intelligence of children in the fields of mathematics and logic. The rules of this game are to complete the board by filling in the empty cells with hijaiyah letters so that one row, column and block do not contain the same letters. This research aims to solve the hijaiyah sudoku game and represent the solution in graph coloring. The results showed that by randomly placing 47 hijaiyah letters, a single solution was obtained. Each cell in a Sudoku game represents a graph vertex. Two vertices are connected if the two cells contain different letters. The graph representing the solutions of the sudoku game has a chromatic number of 12. There are many ways to color the vertices on the graph represented by the chromatic polynomial kromatik P_G (k) = k(k-1)^12 (k-2)^12 〖(k-3)〗^12 〖(k-4)〗^12 〖(k-5)〗^12 〖(k-6)〗^12 〖(k-7)〗^12 〖(k-8)〗^12 〖(k-9)〗^12 〖(k-10)〗^12 〖(k-11)〗^12 with a result of 1963586×e^92 coloring ways. Furthermore, based on the experiments that have been carried out, the game Sudoku hijaiyah size 12 × 12 has more than one solution if the number of letters that appear is less than 47 letters.

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