Wiener Related Index of Gear Fan and Gear Wheel Related Graph

Yun Gao1, Tianwei Xu2, Li Liang2, Wei Gao2

1Department of Editorial, Yunnan Normal University, Kunming 650092, CHINA

2School of Information Science and Technology, Yunnan Normal University, Kunming 650500, CHINA

Abstract: The modified Wiener index and l -modified hyper-Wiener index as extensions of Wiener index, are an important topological index in Chemistry. It is used for the structure of molecule. There is a very close relation between the physical, chemical characteristics of many compounds and the topological structure of that. The modified Wiener index and l -modified hyper-Wiener index are such topological indices and it has been widely used in Chemistry fields. In this paper, based on previous studies, we determine the modified Wiener index and l  modified hyper-Wiener index of gear fan graph, gear wheel graph and their r-corona raphs. The theoretical conclusions obtained in this paper illustrate the promising prospects of the application for the pharmacy and chemical engineering.

Keywords: Chemical Graph Theory; Organic Molecules; Modified Wiener Index; l -modified Hyper- Wiener Index; r-corona Graph