New necessary and sufficient condition and algorithm for directed hamiltonian graph based on boolean determinant theory

摘要

In this paper, a Boolean determinant is introduced, and some properties of the determinants are discussed in Boolean algebra. Next, applying with the properties of characteristic determinant of directed graph, a new Hamiltonian-cycles decision theorem and a new necessary and sufficient conditions for a Hamiltonian directed graph are studied, and a new Hamiltonian-cycles decision algorithm is established. Finally, an example is provided. The obtained results seem to be general in nature.