Structural synthesis of Assur groups with up to 12 links and creation of their classified databases

Abstract

The present study proposes a systematic method for synthesizing a complete set of Assur groups with different links. Moreover, the corresponding databases, including all classified topological structures of synthesized Assur groups, are created. In this regard, the structural correlation and the topological representation of Baranov trusses and Assur groups are initially reviewed. Then, the primary and the secondary vertex-classified sets are introduced to reduce the times of isomorphism identification in the Assur group synthesis. Based on the vertex-symmetry codes used for the isomorphism identification, the systematic synthesis procedure is proposed to achieve all non-isomorphic Assur groups derived from the corresponding Baranov trusses. Finally, a complete set of Assur groups with 2, 4, 6, 8, 10 and 12 links is obtained and three corresponding databases of all synthesized Assur groups are established in accordance with their classified structural characteristics.