The Wiener index of a graph G is the sum of all distances between distinct vertices of the graph G. Singly and doubly vertex weighted Wiener polynomials are generalizations of both vertex weighted Wiener numbers and the ordinary Wiener polynomial. In this paper, we compute the singly and doubly vertex polynomials and their corresponding Wiener numbers of the subdivision graph and the line graph of subdivision graph of the wheel graph.

subdivision graphs, line graphs, wheel   Wiener number, Wiener polynomial, singly and doubly vertex weighted Wiener polynomials.