Using high-performance computations for studying modified bubble-sort graphs

The definition of the Cayley graph was given by the famous English mathematician Arthur Cayley in the XIX century to represent algebraic group defined by a fixed set of generating elements. At present, Cayley graphs are widely used both in mathematics and in applications. In particular, these graphs are used to represent computer networks, including the modeling of topologies of multiprocessor computer systems - supercomputers. This is due to the fact that Cayley graphs have many attractive properties such as regularity, vertex transitive, small diameter and degree at a sufficiently large number of vertices in the graph. For example, such a basic network topology as the “ring”, “hypercube” and “torus” are the Cayley graphs. Using supercomputer computations we obtained the previously unknown characteristics of modified bubble-sort Cayley graphs of dimensions 14 and 15.