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 derive degree base 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. Then we derived some closed formulas for well-known topological indices, first Zagreb index $M_1(G),$ second Zagreb index $M_2(G),$ second modified Zagreb index $m{M}_2(G),$ general Randic index $R_{\alpha }(G),$ Symmetric division index SDD(G), Harmonic index H(G), Inverse Sum index I(G) for polyphenylene 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，我们可以推导出度数基础拓扑指数。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，我们确定了聚苯撑分子结构的M-多项式。然后我们导出了一些著名的拓扑指数的封闭公式，首先是萨格勒布指数${米}_1(G),$第二个萨格勒布指数${米}_2(G),$第二次修改萨格勒布指数$米{米}_2(G),$一般兰迪克指数$R_{\alpha }(G),$分子聚苯撑结构的对称除法指数 SDD(G)、谐波指数H ( G )、逆和指数I ( G )。