Some new concepts, such as the perimeter loop, the maximum perimeter degree-sequence, and the perimeter topological graph, are first presented in this paper, and the method for obtaining the perimeter loop is also involved. Then, based on the perimeter topological graph and some rules for relabeling its vertices canonically, a one-to-one descriptive method, the canonical adjacency matrix set of kinematic chains, is proposed. Another very important characteristic of the descriptive method is that in the canonical adjacency matrix set the element number is reduced dramatically, usually to only one. After that, an effective method to identify isomorphism of kinematic chains is given. Finally, some typical examples of isomorphism identification including two 28-vertex topological graphs are presented in this paper.

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September 2007

Research Papers

# The Establishment of the Canonical Perimeter Topological Graph of Kinematic Chains and Isomorphism Identification

Zhen Huang

Zhen Huang

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Huafeng Ding

Zhen Huang

*J. Mech. Des*. Sep 2007, 129(9): 915-923 (9 pages)

**Published Online:**September 9, 2006

Article history

Received:

April 13, 2006

Revised:

September 9, 2006

Citation

Ding, H., and Huang, Z. (September 9, 2006). "The Establishment of the Canonical Perimeter Topological Graph of Kinematic Chains and Isomorphism Identification." ASME. *J. Mech. Des*. September 2007; 129(9): 915–923. https://doi.org/10.1115/1.2748451

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