Abstract

The complex network models have been widely used to understand mathematical characteristics of Titanium Dioxide Nanotube. Titanium Dioxide Nanotube is a well-known semiconductor and has several industrial and scientific applications. A nanostructure belong to a significant and an extensively investigated compounds in chemical science. It has been derived through engineering mechanism at the molecular scale. The most significant of these new materials are single-walled Titanium Dioxide Nanotube (SWTNT). They have remarkable electronic properties and many other unique characteristics. To compute and study topological indices of nanostructures is a respected problem in nanotechnology. Quantitative structure-property and structure-activity relationships of the single-walled Titanium Dioxide Nanotube (SWTNT) compounds necessitate expressions for the molecular topological features of these compounds. Topological indices are vital devices for investigating chemical compounds to comprehend the fundamental topology of chemical structures. Ev-degree and ve-degree based topological indices are two novel degrees based indices as of late defined in graph theory. Ev-degree and ve-degree based topological indices have been defined as corresponding to their relating partners. In this paper, we have computed topological indices based on ev-degree and ve-degree for the two dimensional lattice of three-layered single-walled Titanium Dioxide Nanotube (SWTNT).

Graphic Abstract

Titanium nanotube is a well-known semiconductor and has several industrial and scientific applications. A nanostructure belong to a significant and an extensively investigated compounds in chemical science. It has been derived through engineering mechanism at the molecular scale. Quantitative structure-property and structure-activity relationships of the single-walled Titanium nanotubes (SWTNT) compounds necessitate expressions for the molecular topological features of these compounds. Ev-degree and ve-degree based topological indices have been defined as corresponding to their relating partners. In this paper, we have computed topological indices based on ev-degree and ve-degree for the two dimensional lattice of three-layered single-walled Titanium nanotubes (SWTNT).

中文翻译：

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基于Ve和Ev度的单壁二氧化钛纳米管的拓扑性质

摘要

复杂的网络模型已被广泛用于理解二氧化钛纳米管的数学特性。钛白粉纳米管是众所周知的半导体，具有多种工业和科学应用。纳米结构属于化学科学中一个重要且经过广泛研究的化合物。它是通过分子机理的工程机理而衍生的。这些新材料中最重要的是单壁二氧化钛纳米管（SWTNT）。它们具有卓越的电子性能和许多其他独特的特性。计算和研究纳米结构的拓扑指数是纳米技术中一个值得关注的问题。单壁二氧化钛纳米管（SWTNT）化合物的定量结构性质和结构活性关系需要表达这些化合物的分子拓扑特征。拓扑指数是研究化学化合物以了解化学结构基本拓扑的重要手段。基于e度和ve度的拓扑索引是最近在图论中定义的两个基于度的新颖索引。基于Ev度和ve度的拓扑索引已定义为与其相关伙伴相对应。在本文中，我们基于ev度和ve度计算了三层单壁二氧化钛纳米管（SWTNT）的二维晶格的拓扑指数。拓扑指数是研究化学化合物以了解化学结构基本拓扑的重要手段。基于e度和ve度的拓扑索引是最近在图论中定义的两个基于度的新颖索引。基于Ev度和ve度的拓扑索引已定义为与其相关伙伴相对应。在本文中，我们基于ev度和ve度计算了三层单壁二氧化钛纳米管（SWTNT）的二维晶格的拓扑指数。拓扑指数是研究化学化合物以了解化学结构基本拓扑的重要手段。基于e度和ve度的拓扑索引是最近在图论中定义的两个基于度的新颖索引。基于Ev度和ve度的拓扑索引已定义为与其相关伙伴相对应。在本文中，我们基于ev度和ve度计算了三层单壁二氧化钛纳米管（SWTNT）的二维晶格的拓扑指数。基于e-度和ve-度的拓扑指数已定义为与其相关伙伴相对应。在本文中，我们基于ev度和ve度计算了三层单壁二氧化钛纳米管（SWTNT）的二维晶格的拓扑指数。基于Ev度和ve度的拓扑索引已定义为与其相关伙伴相对应。在本文中，我们基于ev度和ve度计算了三层单壁二氧化钛纳米管（SWTNT）的二维晶格的拓扑指数。

图形摘要

钛纳米管是一种众所周知的半导体，具有多种工业和科学应用。纳米结构属于化学科学中一个重要且经过广泛研究的化合物。它是通过分子机理的工程机理而衍生的。单壁钛纳米管（SWTNT）化合物的定量结构-性质和结构-活性关系需要表达这些化合物的分子拓扑特征。基于Ev度和ve度的拓扑索引已定义为与其相关伙伴相对应。在本文中，我们基于ev度和ve度计算了三层单壁钛纳米管（SWTNT）的二维晶格的拓扑指数。