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TECHNICAL BRIEFS

A New Method for Detection of Graph Isomorphism Based on the Quadratic Form

[+] Author and Article Information
P. R. He, W. J. Zhang

Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Canada S7N 5A9

Q. Li, F. X. Wu

School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798

J. Mech. Des 125(3), 640-642 (Sep 04, 2003) (3 pages) doi:10.1115/1.1564574 History: Received April 01, 2001; Revised April 01, 2002; Online September 04, 2003
Copyright © 2003 by ASME
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References

Dobrjanskyi,  L., and Freudenstein,  F., 1967, “Some Applications of Graph Theory to the Structural Analysis of Mechanisms,” ASME J. Ind., 89B, pp. 153–158.
Mruthyunjaya,  T. S., and Raghavan,  M. R., 1979, “Structural Analysis of Kinematic Chains and Mechanisms Based on Matrix Representation,” ASME J. Mech. Des., 101, pp. 488–494.
Zhang,  W. J., and Li,  Q., 1999, “On a New Approach to Mechanism Topology Identification,” ASME J. Mech. Des., 121, pp. 57–64.
Randic,  M., 1974, “On the Recognition of Identical Graphs Representing Molecular Topology,” J. Chem. Phys., 60, pp. 3920–3928.
Uicker,  J. J., and Raicu,  A., 1975, “A Method for the Identification and Recognition of Equivalence of Kinematic Chains,” Mech. Mach. Theory, 10, pp. 375–383.
Yan,  H. S., and Hall,  A. S., 1981, “Linkage Characteristic Polynomials: Definitions, Coefficients by Inspection,” ASME J. Mech. Des., 103, pp. 578–584.
Shah,  Y. J., Davida,  G. I., and McCarthy,  M. K., 1974, “Optimum Features and Graph isomorphism,” IEEE Trans. Syst. Man Cybern., 4, pp. 313–319.
Ambekar,  A. G., and Agrawal,  V. P., 1987, “Canonical Numbering of Kinematic Chains and Isomorphism Problem: min Code,” Mech. Mach. Theory, 22, pp. 453–461.
Tang,  C. S., and Liu,  T., 1993, “The Degree Code—A New Mechanism Identifier,” ASME J. Mech. Des., 115, pp. 627–630.
Luo, Y. F., Yang, T. L., and Cao, W. Q., 1991, “Identification on Spatial Kinematic Chains Using Incident Degree and Incident Degree Code,” Proc. of Eighth World Congress on the Theory of Machines and Mechanisms IFToMM’91, Prague, Czechoslovakia, pp. 999–1002.
Mruthyunjava,  T. S., and Balasubramanian,  H. R., 1987, “In Quest of a Reliable and Efficient Computational Test for Detection of Isomorphism in Kinematic Chains,” Mech. Mach. Theory, 22, pp. 131–139.
He, P. R., Zhang, W. J., and Li, Q., 2002, “Eigenvalue and Eigenvector Information of Graphs and Their Validity in Detection of Graph Isomorphism,” Proc. of the 2002 ASME DETC, DETC2002/MECH-34247, Montreal, Canada.

Figures

Grahic Jump Location
Two nonisomorphic kinematic chains both with ten-links
Grahic Jump Location
Two isomorphic graphs both with 17 nodes
Grahic Jump Location
Two nonisomorphic kinematic chains both with twelve bars
Grahic Jump Location
Two nonisomorphic kinematic chains both with ten bars
Grahic Jump Location
Two isomorphic graphs both with 28 nodes

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