Huang, Yufei Bounds on the structural indices of primitive non-powerful generalized sign pattern matrices. (Chinese. English summary) Zbl 1449.15078 J. South China Norm. Univ., Nat. Sci. Ed. 52, No. 1, 91-99 (2020). Summary: In view of the special effects of “loop” in the study of structural index problems, two classes of special generalized signed digraphs are defined: primitive non-powerful generalized signed digraphs with intersecting cycles structure and that with distinguished intersecting cycles structure, respectively. With restriction on primitive nonpowerful generalized signed digraphs with intersecting cycles structure and those with distinguished intersecting cycles structure, upper bounds on the structural indices, e.g. \(k\)th local \(\tau\)-base, \(k\)th same \(\tau\)-base, \(k\)th lower \(\tau\)-base, \(k\)th upper \(\tau\)-base and \(\omega\)-indecomposable base, are discussed by imitating the digraphs, analyzing the ambiguous reachable set and using the properties of Frobenius numbers, respectively. MSC: 15B35 Sign pattern matrices 05C20 Directed graphs (digraphs), tournaments 05C22 Signed and weighted graphs Keywords:generalized sign pattern matrix; generalized signed digraph; structural indices PDFBibTeX XMLCite \textit{Y. Huang}, J. South China Norm. Univ., Nat. Sci. Ed. 52, No. 1, 91--99 (2020; Zbl 1449.15078) Full Text: DOI