some new results on the hosoya polynomial of graph operations

the wiener index is a graph invariant that has found extensive application in chemistry. inaddition to that a generating function, which was called the wiener polynomial, who’sderivate 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] attainedwhat graph operations do to the wiener polynomial. by considering all the results that saganet al. admitted for wiener polynomial on graph operations for each two connected andnontrivial graphs, in this article we focus on deriving wiener polynomial of graph operations,join, cartesian product, composition, disjunction and symmetric difference on n graphs andwiener indices of them.