本原不可幂广义符号矩阵的若干结构指数的界 |
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引用本文: | 黄宇飞.本原不可幂广义符号矩阵的若干结构指数的界[J].华南师范大学学报(自然科学版),2020,52(1):91-99. |
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作者姓名: | 黄宇飞 |
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作者单位: | 广州民航职业技术学院人文社科学院, 广州 510403 |
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摘 要: | 鉴于“环”在结构指数问题研究中的特殊功效, 定义了2类特殊的广义带号有向图:含交圈结构/含违规交圈结构的本原不可幂广义带号有向图.利用有向图的模拟、模糊可达集的分析以及Frobenius数的若干性质, 研究了k点τ-基指数、k点τ-同位基指数、第k重下τ-基指数、第k重上τ-基指数及ω-不可分基指数等结构指数分别在含交圈结构/含违规交圈结构的本原不可幂广义带号有向图类限制下的上界估值问题.
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关 键 词: | 本原 不可幂 (广义)符号矩阵 (广义)带号有向图 结构指数 |
收稿时间: | 2019-01-25 |
Bounds on the Structural Indices of Primitive Non-powerful Generalized Sign Pattern Matrices |
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Institution: | The School of Humanities and Social Sciences, Guangzhou Civil Aviation College, Guangzhou 510403, China |
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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. |
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