The kth upper and lower bases of primitive nonpowerful minimally strong signed digraphs |
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| Authors: | Yanling Shao Jian Shen Yubin Gao |
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| Affiliation: | 1. Department of Mathematics , North University of China , Taiyuan , Shanxi 030051 , P.R. China ylshao@nuc.edu.cn;3. Department of Mathematics , Texas State University , San Marcos , TX 78666 , USA;4. Department of Mathematics , North University of China , Taiyuan , Shanxi 030051 , P.R. China |
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| Abstract: | In this article, we study the kth upper and lower bases of primitive nonpowerful minimally strong signed digraphs. A bound on the kth upper bases for primitive nonpowerful minimally strong signed digraphs is obtained, and the equality case of the bound is characterized. For the kth lower bases, we obtain some bounds. For some cases, the bounds are best possible and the extremal signed digraphs are characterized. We also show that there exist ‘gaps’ in both the kth upper base set and the kth lower base set of primitive nonpowerful minimally strong signed digraphs. |
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| Keywords: | base sign pattern digraph primitive matrix nonpowerful |
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