The initial path-operation matrix and general path-operation matrix were derived from the adjacent matrix of a simple graph.The addition and multiplication operation of the general path-operation matrices were defined,which can be used to solve some path problems,such as the longest path,the shortest path,the path between any two points,and path problems with length constraints.This method can also determine whether Hamilton cycles exist or not and if they exist can find out all of them.The desired results were all showed in the final path-operation matrices.The power length formula of general...
