Bounds on the Structural Indices of Primitive Non-powerful Generalized Sign Pattern Matrices

HUANG Yufei

doi:10.6054/j.jscnun.2020014

Journal of South China Normal University (Natural Science Edition) > 2020 > 52(1): 91-99. > DOI: 10.6054/j.jscnun.2020014

HUANG Yufei. Bounds on the Structural Indices of Primitive Non-powerful Generalized Sign Pattern Matrices[J]. Journal of South China Normal University (Natural Science Edition), 2020, 52(1): 91-99. DOI: 10.6054/j.jscnun.2020014

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Bounds on the Structural Indices of Primitive Non-powerful Generalized Sign Pattern Matrices

HUANG Yufei^,

The School of Humanities and Social Sciences, Guangzhou Civil Aviation College, Guangzhou 510403, China

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Received Date: January 24, 2019
Available Online: March 21, 2021

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Abstract

Abstract

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 non-powerful generalized signed digraphs with intersecting cycles structure and those with distinguished intersecting cycles structure, upper bounds on the structural indices, e.g. kth local τ-base, kth same τ-base, kth lower τ-base, kth upper τ-base and ω-indecomposable base, are discussed by imitating the digraphs, analyzing the ambiguous reachable set and using the properties of Frobenius numbers, respectively.
- primitive,
- non-powerful,
- (generalized) sign pattern matrix,
- (generalized) signed digraph,
- structural indices

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