Parallel processing and supercomputing continue to exert great influence in the development of modern science and engineering. The network of processors and interconnections play a vital role in facilitating the communication between processors in a parallel computer. Some of the popular interconnection schemes are rings, toroids and hypercubes. Their popularity stems from the commercial availability of machines with these architectures. These three families of graphs viz., rings, toroids and hypercubes share a common property of being a Cayley graph. Many important problems in networks have...

Matrices play a vital role in modeling because of the rich techniques available in the domain of matrices. In this aspect, role of the inverse of a matrix is very important and is the fundamental for solution techniques. For a given matrix, the Moore-Penrose inverse is the unique matrix satisfying four fundamental matrix equations. The concept of unitary matrices for non-singular category has been extended as partial isometry to rectangular matrices, via the tool of Moore-Penrose inverses. This beginning has subsequently extended the concept of partial isometry to star-dagger matrices, which...