Abstract: The graph isomorph judgement problem in graph theory is yet to be solved. A series of properties for the quicker judgement on whether two graphs are isomorphic were obtained through the permutation of rows and columns of adjacent matrix of graphs. A search algorithm on graph isomorph judgement was proposed on the basis of several properties. Then two examples were presented to explain and demonstrate the algorithm for better understanding of these properties and the algorithm. Finally a brief conclusion and the further research direction were presented.