[01] Yun Gao, Department of Editorial, Yunnan Normal University, Kunming, China. [02] Sainan Zhou, Zhejiang Zhenyuan Pharmaceutical Co., Ltd, Shaoxing, China. [03] Wei Gao, School of Information Science and Technology, Yunnan Normal University, Kunming, China.

Chemical compounds and drugs are often modelled as graphs (for example, Polyhex Nanotubes and Dendrimer Nanostar) where each vertex represents an atom of molecule and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph and can be different structures. The edge Wiener index of a graph is defined as the sum of the distances between all pairs of edges, and it has been found extensive applications in chemistry. In this paper, we determine the edge Wiener index of gear fan graph, gear wheel graph and their r-corona graphs.

Organic Molecules, Edge Wiener Index, Fan Graph, Wheel Graph, Gear Fan Graph, Gear Wheel Graph, r-Corona Graph

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