On a composition of digraphs

Many "good" topologies for interconnection networks are based on line digraphs of regular digraphs. These digraphs support unitary matrices. We propose the property "being the digraph of a unitary matrix" as additional criterion for the design of new interconnection networks. We define a composition of digraphs, which we call diagonal union. Diagonal union can be used to construct digraphs of unitary matrices. We remark that digraphs obtained via diagonal union are state split graphs, as defined in symbolic dynamics. Finally, we list some potential directions for future research.Comment: 6 pages, 1 figure. Abstract accepted for the Third Haifa Workshop on Interdisciplinary Applications of Graph Theory, Combinatorics and Algorithms, May 27-29, 2003, Haifa, Israe