yy-Wiener index of composite graphs

Eliasi and Taeri [Extension of the Wiener index and Wiener polynomial, Appl. Math. Lett. 21 (2008) 916–921] introduced the notion of yy-Wiener index of graphs as a generalization of the classical Wiener index and hyper Wiener index of graphs. They obtained some mathematical properties of this new defined topological index. In this paper, the join, Cartesian product, composition, disjunction and symmetric difference of graphs under yy-Wiener index are computed. By these results most parts of a paper by Sagan et al. [The Wiener polynomial of a graph, Int. J. Quant. Chem. 60 (1996) 959–969] and another paper by Khalifeh et al. [The hyper-Wiener index of graph operations, Comput. Math. Appl. 56 (2008) 1402–1407] are generalized.