Generation of Structural Lattices through Cartesian Product of Grid Graphs

The paper deals with topological models of structural lattices i.e. graphs. Examples of transformations of structural lattices obtained through manipulation on the structure of graphs are presented. Specifically, examples of such operations as deleting of the edge, contraction of vertices and opposite transformations are considered. Another operation that allows transforming graphs, is their multiplication (Cartesian product). It has been shown, that every connected graph of finite type has unique factor decomposition with respect to Cartesian multiplication, and that the automorphism group of any such graph is isomorphic to the automorphism group of the sum of its prime factors. For the presented transformations it is important that they do not violate Steinitz’s theorem which states that a graph is 3D realizable if and only if it is planar and 3-connected with edges in every vertex. Composition of transformed graphs allows prediction of its structural properties.