The Graph Isomorphism Algorithm: Graph Isomorphism is in P
Aug 2009 · Institute of Mathematics
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About this ebook
We present a new polynomial-time algorithm for determining whether two given graphs are isomorphic or not. We prove that the algorithm is necessary and sufficient for solving the Graph Isomorphism Problem in polynomial-time, thus showing that the Graph Isomorphism Problem is in P. The semiotic theory for the recognition of graph structure is used to define a canonical form of the sign matrix of a graph. We prove that the canonical form of the sign matrix is uniquely identifiable in polynomial-time for isomorphic graphs. The algorithm is demonstrated by solving the Graph Isomorphism Problem for many of the hardest known examples. We implement the algorithm in C++ and provide a demonstration program for Microsoft Windows.
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About the author
Ashay Dharwadker is the Distinguished Professor of Mathematics & Natural Sciences at the Institute of Mathematics, Gurgaon, India. He is the author of a dozen exquisitely illustrated books describing his fundamental contributions to combinatorics, graph theory, computer science and the foundations of physics.
John-Tagore Tevet is an Honorary Professor at the Institute of Mathematics, Gurgaon and Distinguished Professor at the Structure Semiotics Research Group S.E.R.R., Euroacademy, Tallinn.
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