Abstract—In theoretical chemistry, the revised Szeged index and revised Szeged edge index were introduced to measure the stability of alkanes and the strain energy of cycloalkanes. In this paper, by virtue of mathematical derivation, we determine the revised Szeged index and revised edge Szeged index of fan molecular graph, wheel molecular graph, gear fan molecular graph, gear wheel molecular graph, and their r-corona molecular graphs. These molecular structures are widely used in biology, medical science and pharmaceutical fields. At last, the normalized revised Szeged indexes of fan molecular graph, wheel molecular graph, gear fan molecular graph, gear wheel molecular graph, and their r-corona molecular graphs are given.

Index Terms—Chemical graph theory, revised Szeged index, revised edge Szeged index, fan molecular graph, wheel molecular graph, gear fan molecular graph, Gear wheel molecular graph, r-corona molecular graph.

Yun Gao is with the Department of Editorial, Yunnan Normal University, Kunming 650092, China.
Wei Gao and Li Liang are with School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China (e-mail: gaowei@ynnu.edu.cn).

Cite: Yun Gao, Wei Gao, and Li Liang, "Revised Szeged Index and Revised Edge Szeged Index of Certain Special Molecular Graphs," International Journal of Applied Physics and Mathematics vol. 4, no. 6, pp. 417-425, 2014.