The Bases and Base Set of Primitive Symmetric Loop-Free Signed Digraphs

摘要

In this paper,we study the bases and base sets of primitive symmetric loop-free (generalized) signed digraphs on n vertices.We obtain sharp upper bounds of the bases,and show that the base sets of the classes of such digraphs are {2,3,...,2n - 1｝.We also give a new proof of an important result obtained by Cheng and Liu.