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In this paper, we study the kth upper bases of primitive non-powerful signeddigraphs. A bound on the kth upper bases of all primitive non-powerful signeddigraphs is obtained, and the equality case of the bound is characterized. Wealso show that there exists "gap" in the kth upper base set of primitivenon-powerful signed digraphs.

The kth Upper Bases of Primitive Non-powerful Signed Digraphs