一些标准图的单声碎数
1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India.
Heliyon
|June 7, 2024
概括
这项研究在图形理论中引入了单声碎数. 它定义了任何顶点需要的最小小石头,可以通过单声路径使用碎石移动到达顶点.
科学领域:
- 图形理论 图形理论
- 组合学是一种组合学.
- 离散的数学 离散的数学
背景情况:
- 图形碎是一种新的概念,涉及到在图形顶点上的卵石操纵.
- 现有的瓦定义缺乏路径约束.
- 单声路径,不重复顶点,在网络分析中至关重要.
研究的目的:
- 介绍和定义单声碎号码的新概念.
- 为了确定通过单声路径保证可达到的最低小石头数量.
- 分析这个新的图形在标准和衍生图形上不变的边界.
主要方法:
- 定义单声破碎数 (m) 为可达到的最小小石头.
- 应用碎石移位,其中一个石被添加到一个顶点,并从两个邻居中移除.
- 在特定的图形结构上计算单声滚动数的上下限.
主要成果:
- 首次正式定义了单音号码.
- 介绍了计算其上限和下限的方法.
- 在标准和衍生图表上分析了不变量的行为.
结论:
- 在特定路径约束下,单声碎号为图形连接提供了一个新的指标.
- 这项研究奠定了进一步研究图形理论中滚动不变量的基础.
- 了解这些数字可能会对网络的稳定性和设计产生影响.
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