Some Special Digraphs Broad Base

Graph theory is an important branch of mathematics, the research object is graph. In this paper, we study the local bases and kth upper bases of two kind of primitive non-powerful signed digraphs, and the bounds of the first generalized primitive exponents of a class of two-colored digraphs.In the first chapter, we introduce the development of the digraph, some results in literatures relate to this paper and the main results in this paper.The second chapter we discuss a kind of primitive non-powerful signed digraphs, the local exponents and bases of the kind of primitive non-powerful signed digraphs are obtained.Chapter 3 we discuss a kind of n(n≥7) order primitive non-powerful signed digraphs, the kth upper bases of primitive non-powerful signed digraphs are obtained. The fourth chapter discuss a class of two-colored signed digraphs with three cycles, get the bounds of the first generalized primitive exponents of the class of two-colored digraphs.