Orthogonal graphs for the construction of a class of interconnection networks

A graph theoretical representation for a class of interconnection networks is suggested. The idea is based on a definition of orthogonal binary vectors and leads to a construction rule for a class of orthogonal graphs. An orthogonal graph is first defined as a set of 2 ^m nodes, which in turn are linked by 2^m-n edges for every link model defined in an integer set Q*. The degree and diameter of an orthogonal graph are determined in terms of the parameters n, m, and the number of link modes defined in Q*. Routing in orthogonal graphs is shown to reduce to the node covering problem in bipartite graphs. The proposed theory is applied to describe a number of well-known interconnection networks such as the binary m-cube and spanning-bus meshes. Multidimensional access (MDA) memories are also shown as examples of orthogonal shared memory multiprocessing systems. Finally, orthogonal graphs are applied to the construction of multistage interconnection networks. Connectivity and placement rules are given and shown to yield a number of well-known networks