Sharif Digital Repository

Since critical and defining sets have been examined in various fields of combinatorics, including Latin squares and different branches of graph theory, we aim to present a portion of the obtained results con-cerning defining sets in diverse fields of graph theory, and provide a survey on them.In the present dissertation, we examine defining sets of vertex coloring,edge coloring, total coloring and forcing sets of orientation of graphs,perfect matching, hull and geodetic sets. Since complete graphs’ col-oring defining sets and Latin squares’ critical sets are closely related,we shall discuss them in a coloring framework. Furthermore, for dif-ferent graph families, including regular graphs,... 

Sudoku is an intellectual game based on mathematics. Sudoku achieved global fame in a short time because this game doesn’t need any mathematical operation like addition and multiplication and in theory, instead of numbers, lechers, shapes,colors, etc. could be placed.Sudoku which is a single-player game in generally the player should complete a partial n2 × n2 matrix M all of whose enteries are drawn from {1; 2,..., n2} by applying the rules: no number may appear more than once in any row, any column,or any of the nine ‘‘blocks’’. Actually blocks are n × n submatrixs with indices {na + 1, na + 2,…, na + n} × {nb + 1, nb + 2,….., nb + n} Actually, A Sudoku is A Latin square with one...