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, distance-based 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 structure-property relationships in a series of acyclic and cycle-containing 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) 235-244].