The kth Upper Bases of Primitive Non-powerful Signed Digraphs ∗

In this paper, we study the kth upper bases of primitive non-powerful signed digraphs. A bound on the kth upper bases of all primitive non-powerful signed digraphs is obtained, and the equality case of the bound is characterized. We also show that there exists “gap ” in the kth upper base set of primitive non-powerful signed digraphs. AMS classification: 05C20, 05C50, 15A4