new graph products for configuration processing

for the analysis of structures, the first step consists of configuration processing followed by data generation. this step is the most time consuming part of the analysis for large-scale structures. in this paper new graph products called triangular and circular graph products are developed for the formation of the space structures. the graph products are extensively used in graph theory and combinatorial optimization, however, the triangular and circular products defined in this paper are more suitable for the formation of practical space structural models which can not be generated easily by the previous products. the new products are employed for the configuration processing of space structures that are of triangular or a combination of triangular and rectangular shapes, and also in circular shapes as domes and some other space structural models. cut out products are other new types of graph products which are defined to eliminate all of the connected elements to the considered node to configure the model or grid with some vacant panels inside of the model. the application of the presented graph products can be extended to the formation of finite element models.