Math and Sudoku: Exploring Sudoku boards through graph theory, group theory, and combinatorics

Encoding Sudoku puzzles as partially colored graphs, we state and prove Akman’s theorem regarding the associated partial chromatic polynomial; we count the 4x4 sudoku boards, in total and fundamentally distinct; we count the diagonally distinct 4x4 sudoku boards; and we classify and enumerate the different structure types of 4x4 boards.