PI polynomials of product graphs

The Padmakar–Ivan (PI) index of a graph GG is defined as PI(G)=∑[neu(e|G)+nev(e|G)]PI(G)=∑[neu(e|G)+nev(e|G)], where neu(e|G)neu(e|G) is the number of edges of GG lying closer to uu than to vv, nev(e|G)nev(e|G) is the number of edges of GG lying closer to vv than to uu and summation goes over all edges of GG. In this work, the PI polynomial for the Cartesian product graphs is computed.