Some New Results On the Hosoya Polynomial of Graph Operations

شاخص وينر، يك پاياي گراف است كه كاربرد زيادي در شيمي پيدا كرده است. مي توان تابعي مولد با نام چندجمله‌اي وينر براي اين شاخص چنان تعريف نمود كه مشتق آن يك –qآنالوگ شاخص وينر است. ساگان، يه و زانگ در مقاله ي [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959?969] تعدادي از اعمال يك گراف را تحت چندجمله‌اي وينر مورد بررسي قرار دادند. با در نظر گرفتن تمامي آن نتايج ما خود را روي چندجمله‌اي وينر اعمال اتصال، حاصل‌ضرب دكارتي، تركيب، انفصال و تفاضل متقارن n گراف متمركز كرده و شاخص‌هاي وينر آن‌ها را محاسبه مي‌كنيم.

The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959?969] attained what graph operations do to the Wiener polynomial. By considering all the results that Sagan et al. admitted for Wiener polynomial on graph operations for each two connected and nontrivial graphs, in this article we focus on deriving Wiener polynomial of graph operations, Join, Cartesian product, Composition, Disjunction and Symmetric difference on n graphs and Wiener indices of them.