This paper proposes a new method for detection of graph isomorphism using the concept of quadratic form. Graphs/kinematic chains are represented first by quadratic form, and the comparison of two graphs is thus reduced to the comparison of two quadratic form expressions. If both the lengths and the directions of the semiaxes of quadric surfaces, which are characterized by the eigenvalues and eigenvectors, are the same, the associated graphs/kinematic chains are isomorphic. An algorithm is developed based on this idea, and tested for the counter-examples known to other methods.
A New Method for Detection of Graph Isomorphism Based on the Quadratic Form
Contributed by the Mechanisms and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 2001; revised April 2002. Associate Editor: S. K. Agrawal.
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He and , P. R., Zhang , W. J., Li and , Q., and Wu , F. X. (September 4, 2003). "A New Method for Detection of Graph Isomorphism Based on the Quadratic Form ." ASME. J. Mech. Des. September 2003; 125(3): 640–642. https://doi.org/10.1115/1.1564574
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