The Bases And Generalized Bases Of Some Special Classes Of Signed Digraphs

Graph theory is a rapidly developing branch of combinatorial mathematics, its study inmany aspects of social life has a wide application background. The bounds of the bases andlocal bases of some special primitive non-powerful signed digraphs are obtained by analyingthe characteristics of SSSD walks, Frobenius and distinguished cycle pair.In chapter 1, we introduce the history of development on the graph theory, the researchprogress of signed digraphs, basic knowledge and the main work of this paper.In chapter 2, we discuss the bases of two special classes primitive non-powerful signeddigraphs with four simple cycles, and obtain the bounds of the bases.In chapter 3, we study the bases and local bases of a kind of primitive non-powerfulsigned digraphs with three simple cycles, and obtain the bounds of the bases and local basesunder different conditions.