Development of a Standard Code for Colored Graphs and Its Application to Kinematic Chains

[+] Author and Article Information
Jae Kyun Shin, S. Krishnamurty

Department of Mechanical Engineering, University of Massachusetts, Amherst, MA 01003

J. Mech. Des 116(1), 189-196 (Mar 01, 1994) (8 pages) doi:10.1115/1.2919345 History: Received January 01, 1992; Online June 02, 2008


The development of an efficient solution procedure for the detection of isomorphism and canonical numbering of vertices of colored graphs is introduced. This computer-based algorithm for colored graphs is formed by extending the standard code approach developed earlier for the canonical numbering of simple noncolored graphs, which fully utilizes the capabilities of symmetry analysis of such noncolored graphs. Its application to various kinematic chains and mechanisms is investigated with the aid of examples. The method never failed to produce unique codes, and is also found to be robust and efficient. Using this method, every kinematic chain and mechanism, as well as path generators and function generators, will have their own unique codes and a corresponding canonical numbering of their respective links. Thus, based on its efficiency and applicability, this method can be used as a universal standard code for identifying isomorphisms, as well as for enumerating nonisomorphic kinematic chains and mechanisms.

Copyright © 1994 by The American Society of Mechanical Engineers
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