Weighted triangular and circular graph products for configuration processing

Abstract

In this paper new weighted triangular and circular graph products are presented for configuring the new forms of structural models. The graph products are extensively used in graph theory and combinatorial optimization, however, the weighted triangular products defined in this paper are more suitable for the formation of practical space structural models which are impossible to generate by the previous products. Here, the weighted triangular and circular products are employed for the configuration processing of space structures that are of triangular shapes or a combination of triangular and rectangular shapes and also of the solid circler shapes as domes and some space structural models. The covered graph products are represented for selecting or eliminating some parts or panels from the product graph by using the second weights for the nodes of the generators. Cut out products are other new types of graph products which are defined to eliminate all of the connected elements to a specified node, to configure the model or grid with some vacant panels inside of the model. This application can easily be extended to the formation of finite element models.