Abstract: The concepts of associated graph G and associated hypergraph H are introduced for a switching function F(x1,,xn) with n variables. Then, the following methods and algorithms are derived: (1) The graph theory methods and branch-and-bound algorithm BBAPI for finding all prime implicants of F, (2) Algorithm AMSHT for finding a minimal sum for F by hypergraph theory. These methods are simple and intuitive. They are convenient not only for computation by hand but also for realization by a computer. Their computation efficency are higher than that of Karnaugh map method and Q-M tabular method which are customarily used.