Canonical numbering of kinematic chains and isomorphism problem: min code

Some further development on the eigensystem approach for graph isomorphism detection

“…This integer number uniquely corresponds to the graph and the labeling of the vertices of the graph. There exists a unique maximum number defined as max code of the graph [18], and there also exists a unique minimum code defined as min code of the graph [19]. Therefore, one can identify GI by comparing these unique or canonical codes of two graphs.…”

A new theory for the topological structure analysis of kinematic chains and its applications

“…But they are only the necessary condition for isomorphism identification and several counter-examples have been found [9]. The min-code method [11] requires a complicated analysis of distance matrix as well as the connectivity matrix to start its procedure. The Hamming-number approach [12][13][14] introduced a new idea for isomorphism identification and topological structure analysis.…”

Generating functions for mechanism specialization

“…In this latter, each kinematic chain is specialized through the assignation of link and joint types to obtain all possible mechanism configurations. Type synthesis and mechanism specialization have been the subject of many studies , which have variously based the structural synthesis of the kinematic chains on the graph theory [2][3][4][5][6][7][8][9], a characteristic polynomial [10][11][12][13][14][15][16], or approaches based on codes [17][18][19][20][21][22][23][24][25], matrices [26][27][28], or other elements [29][30][31][32][33][34][35][36][37][38][39]. In some such investigations, a generation of the multiple kinematic chains or mechanisms during the synthesis and specialization processes requires complex procedures for the detection (or computer-aided assignation) and deletion of isomorphic mechanisms [40][41][42].…”