A new method for isomorphism identification in topological graphs using incident matrices

• Published in: Mechanism and machine theory Vol. 49; pp. 298 - 307
• Main Authors: Yang, Fei, Deng, Zongquan, Tao, Jianguo, Li, Lifang
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.03.2012; Elsevier
• Subjects: Adjacency matrices; Applied sciences; Computer science; control theory; systems; Drives; Exact sciences and technology; Graph invariants; Graphs; Information retrieval. Graph; Isomorphism; Kinematic chains; Linkage mechanisms, cams; Mathematical analysis; Matrices; Matrix methods; Mechanical engineering. Machine design; Necessary and sufficient condition; Theoretical computing; Topology; Vertex sequence; Kinematic chains; Necessary and sufficient condition; Graph invariants; Vertex sequence; Adjacency matrices; Invariant; Sufficiency; Topological graph; Adjacency matrix; Graph theory; Topology; Isomorphism; Kinematic chain; Reliability
• ISSN: 0094-114X; 1873-3999
• DOI: 10.1016/j.mechmachtheory.2011.09.008

A new method using incident matrices to identify the isomorphism of topological graphs is proposed in this paper. The technique of acquiring the necessary condition for identifying the isomorphism is developed by comparing the calculation of incident matrices. Furthermore, it can be automatically executed by programs. With the help of the results from the necessary condition, the technique to find the correspondence of different vertices is presented, and the sufficiency for the isomorphism identification is obtained. Three examples are presented to demonstrate the validity and reliability of this method. ► We developed a new method to detect the isomorphism with structural synthesis. ► Using incident matrices, the necessary condition was obtained. ► On the basis of the necessary condition, the sufficiency was achieved. ► Detail operations to get the sufficient and necessary conditions were given. ► The new method can find the sufficiency quickly, it is effective and reliable.