Shaped lattice graphs as models of the multiprocessor computer systems

A new family of the uniform ordinary graphs named the shaped lattice graphs was proposed and studied. As applied to the structural modeling of the multiprocessor computer systems, they have two useful characteristics such as high flexibility at choosing their size (number of vertices) and possibility of obtaining small (down to $d=2$) diameters independently of the graph size. The method of cycle definition and transformation by the ring sequences of edge weights, which was previously proposed for the binary hypercubes and other Cayley graphs, was extended to the shaped lattice graphs.