Abstract

In a molecular graph, molecules are associated with some numerical values these values are known as topological indices. From the M-polynomial of molecular structure we can derived degree based topological indices. We can derived chemical and physical properties of chemical compound from the topological indices. To find the strain energy, melting point, boiling point, distortion and stability of chemical compound usually mathematician used topological indices. Moreover topological indices also make relation between biological activities of compound with physical properties. In this paper, we determined the M-polynomials of the structure of the molecules of polyphenylene nanotube and nanotori. Then we derived some closed formulas for well-known topological indices, first Zagreb index, second Zagreb index, second Modified Zagreb index $m{M}_2(G),$ general Randić index, Symmetric division index, Harmonic index, inverse sum index for polyphenylene nanotube structure of molecules.

摘要

在分子图中，分子与一些数值相关联，这些数值称为拓扑指数。从分子结构的M多项式中，我们可以推导出基于度数的拓扑指数。我们可以从拓扑指数中推导出化合物的化学和物理性质。为了找到化合物的应变能、熔点、沸点、变形和稳定性，数学家通常使用拓扑指标。此外，拓扑指标也将化合物的生物活性与物理性质联系起来。在本文中，我们确定了M-聚苯纳米管和纳米托里分子结构的多项式。然后我们导出了一些知名拓扑指数的封闭公式，第一个萨格勒布指数，第二个萨格勒布指数，第二个修正萨格勒布指数$米{米}_2(G),$分子聚苯纳米管结构的通用 Randić 指数、对称分裂指数、谐波指数、逆和指数。