Wiener Polarity Index of Tensor Product of Graphs

Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. In theoretical chemistry, distancebased molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. The Wiener Polarity index of a graph G is denoted by W_P (G) is the number of unordered pairs of vertices of distance 3. The Wiener polarity index is used to demonstrate quantitative structureproperty relationships in a series of acyclic and cyclecontaining hydrocarbons. Let G,H be two simple connected graphs. Then the tensor product of them is denoted by G⨂H whose vertex set is V(G⨂H)=V(G)×V(H) and edge set is E(G⨂H)={(a,b)(c,d)| ac∈E(G) ,bd∈E(H) }. In this paper, we aim to compute the Wiener polarity index of G⨂H which was computed wrongly in [J. Ma, Y. Shi and J. Yue, The Wiener Polarity Index of Graph Products, Ars Combin., 116 (2014) 235244].