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普通能量与自循环图的能量之间的关系
B R Rakshith1, Kinkar Chandra Das2, B J Manjunatha3,4
1Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576 104, India.
Heliyon
|March 21, 2024
概括
这项研究为具有自我循环的图形的能量提供了界限,将其与原始图形能量相关联. 它还证明,对双面图的特定能量不等式对不平衡的双面图不适用.
科学领域:
- 图形理论 图形理论
- 谱图理论 谱图理论
- 数学化学 数学化学
背景情况:
- 图形的能量是其稳定性的度量,与其相邻矩阵的固有值有关.
- 自动循环可以改变图的光谱属性和能量.
- 之前的研究已经确定了双边图的能量不平等.
研究的目的:
- 建立一个自动循环图的能量上下界限.
- 为了调查不平衡的双面图形存在的能源不平等的有效性.
主要方法:
- 该研究涉及对图形能量进行理论分析.
- 边界是使用自值和图形结构的属性来导出的.
- 通过矛盾证明了某些不平衡的双面图的不存在.
主要成果:
- 带有自我循环的图的能量新的上下界限以原始图的能量,顶点的数量和自我循环的数量来呈现.
- 证明不等式E ((G) >= E ((G+S) 不适用于不平衡的两部分图形,其中分区中的顶点数量不同.
- 证明了与图形能量相关的特定属性不存在不平衡的双分线图.
结论:
- 具有自我循环的图的能量可以被界定,从而提供了关于自我循环如何影响图的能量的见解.
- 严格的不等式E ((G) >E ((G+S)) 对于不平衡的双面图表来说是正确的,改进了之前的发现.
- 这项研究有助于理解自循环图的光谱属性,特别是在二分位图的背景下.
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