The Bases Of Primitive Non-powerful Signed Digraphs With Three Cycles

Graph theory is an important branch of combinatorial mathematics. It has broadapplication fields which cover computer science, psychology, sociology, traffic management,physics, biology, chemistry, password security, fluid dynamics, telecommunications and soon．In this dissertation, the bases of primitive non-powerful signed digraphs with three cyclesare studied. Exact value of the bases are obtained by analyzing this digraph and using therelated knowledge about reduction to absurdity, Frobenius set, primitive exponent,distinguished cycle pair, SSSD walks, Ambiguous index, diameter of digraph and so on.In chapter 1, we provide a brief introduction to combinatorial mathematics, outline theresearch history of the Graph theory, basic concepts of sign pattern matrixes, signed digraphsand recent developments of signed digraphs. Lastly, we introduce the main conclusion of thisdissertation.From chapter 2 to chapter 4, we obtain exact value of these three classes of the bases ofdigraphs by studying three classes of primitive non-powerful signed digraphs with threecycles respectively.