An Approach of Graph Isomorphism Detection based on Vertex-Invariant

Graph Isomorphism is a widely studied problem due to its practical applications in various fields of networks, chemistry and finger print detection, recent problems in biology such as diabetes detection, protein structure and information retrieval. An approach to the graph isomorphism detection is based on vertex invariant. In the existing approach vertex invariants is used to partition the matrix of input graph for reducing size of decision tree to detect graph isomorphism. In this approach the graph isomorphism detection is carried out by comparing the entire adjacency matrix of input graph with the model graph. Element by element comparisons requires more time to detect graph isomorphism. In this paper we present graph isomorphism detection algorithm based on vertex invariant and Euclidean vector. We evaluate the proposed algorithm on the various randomly generated directed and undirected graphs by computing the Euclidean vector of input graph adjacency matrix and model graph to make comparison with existing algorithm. Experimental result shows that computational time complexity is reduced remarkably as compared to the existing sequential algorithm. Keywords—Graph Isomorphism, Vertex Invariants, Eucledian vector