[01] Yun Gao, Department of Editorial, Yunnan Normal University, Kunming, China. [02] Li Liang, School of Information Science and Technology, Yunnan Normal University, Kunming, China. [03] Wei Gao, School of Information Science and Technology, Yunnan Normal University, Kunming, China.

Chemical compounds and drugs are often modeled as graphs 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. In this paper, we determine the singly vertex-weighted Wiener polynomial and doubly vertex-weighted Wiener polynomial of fan molecular graph, wheel molecular graph, gear fan molecular graph, gear wheel molecular graph, and their r-corona molecular graphs.

Chemical Graph Theory, Singly Vertex-Weighted Wiener Polynomial, Doubly Vertex-Weighted Wiener Polynomial, R-Corona Molecular Graph

[01] L. Yan, Y. Li, W. Gao, J. S. Li, On the extremal hyper-wiener index of graphs, Journal of Chemical and Pharmaceutical Research, 2014, 6(3): 477-481. [02] L. Yan, W. Gao, J. S. Li, General harmonic index and general sum connectivity index of polyomino chains and nanotubes, Journal of Computational and Theoretical Nanoscience, In press. [03] W. Gao, L. Liang, Y. Gao, Some results on wiener related index and shultz index of molecular graphs, Energy Education Science and Technology: Part A, 2014, 32(6): 8961-8970. [04] W. Gao, L. Liang, Y. Gao, Total eccentricity, adjacent eccentric distance sum and Gutman index of certain special molecular graphs, The BioTechnology: An Indian Journal, 2014, 10(9): 3837-3845. [05] W. Gao, L. Shi, Wiener index of gear fan graph and gear wheel graph, Asian Journal of Chemistry, 2014, 26(11): 3397-3400. [06] W. Gao, W. F. Wang, Second atom-bond connectivity index of special chemical molecular structures, Journal of Chemistry, Volume 2014, Article ID 906254, 8 pages, http://dx.doi.org/10.1155/2014/906254. [07] W. F. Xi, W. Gao, Geometric-arithmetic index and Zagreb indices of certain special molecular graphs, Journal of Advances in Chemistry, 2014, 10(2): 2254-2261. [08] W. F. Xi, W. Gao, -Modified extremal hyper-Wiener index of molecular graphs, Journal of Applied Computer Science & Mathematics, 2014, 18 (8): 43-46. [09] W. F. Xi, W. Gao, Y. Li, Three indices calculation of certain crown molecular graphs, Journal of Advances in Mathematics, 2014, 9(6): 2696-2304. [10] Y. Gao, W. Gao, L. Liang, Revised Szeged index and revised edge Szeged index of certain special molecular graphs, International Journal of Applied Physics and Mathematics, 2014, 4(6): 417-425. [11] J. A. Bondy, U. S. R. Mutry, Graph Theory, Spring, Berlin, 2008