This research study the isomorphism problem of two simple planar graphs with same number of vertices and edges, we used the permutations algorithm that generates a permutation from known permutation. The program (in MatLab) has been constructed to compare two graphs by generating all permutations of the vertices of the first graph and finding the adjacency matrix of it in each permutation then compare it with the adjacency matrix of the second graph . Finally the result discusses whether the two graphs are isomorphic or not