Graphs of unitary matrices

The support of a matrix M is the (0, 1)-matrix with ij-th entry equal to 1 if the ij-th entry of M is non-zero, and equal to 0, otherwise. The digraph whose adjacency matrix is the support of M is said to be the digraph of M . This paper observes some structural properties of digraphs and Cayley digraphs, of unitary matrices. We prove that a group generated by two elements has a set of generators such that the Cayley digraph in respect to such a set is the digraph of a unitary matrix. We prove that the digraph of a unitary matrix is without cut-vertices, directed bridges, and bridges; we conjecture that it is hamiltonian. MSC2000: Primary 05C50; Secondary 05C25