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上三角矩阵的零除数图的哈拉里指数
Omaima Alshanqiti1, Sahil Sharma2, Vijay Kumar Bhat3
1Department of Mathematics, Umm al-Qura University, Makkah, Saudi Arabia.
Scientific reports
|February 4, 2026
概括
本研究使用哈拉里指数来量化图形结构,用于从上三角矩阵中衍生的零除法图. 哈拉里指数用于有限的交换式和非交换式环上的有向和无向图.
科学领域:
- 图形理论是指图形的理论.
- 抽象代数的抽象代数.
- 组合学是一种组合学.
背景情况:
- 哈拉里指数是化学图形理论和网络分析中使用的关键图形不变量.
- 零分数图提供了对环的代数结构的视觉表示.
- 上三角矩阵构成一个重要的矩阵类别,在各种数学领域都有应用.
研究的目的:
- 用哈拉里指数量化分析零除数图的结构性质.
- 为了计算与上三角矩阵相关的零除数图的哈拉里指数.
- 为了研究哈拉里指数,针对有定向和无定向的零分数图表.
主要方法:
- 从上方三角矩阵的环中构建零分数图.
- 将哈拉里指数定义应用于这些特定的图形结构.
- 针对指向与非指向图的哈拉里指数的比较分析.
主要成果:
- 哈拉里指数成功计算了上三角矩阵在有限的交换和非交换环上的零除数图.
- 对于有定向和无定向图表表示,观察到哈拉里指数的不同值.
- 该研究提供了对这些代数图的结构复杂性的定量测量.
结论:
- 哈拉里指数是描述零分数图的结构特征的宝贵工具.
- 环的代数结构 (交换性与非交换性) 影响其相关的零除数图的哈拉里指数.
- 这项研究有助于理解代数结构的图形理论性质.
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