 The Padmakar–Ivan index of a graph "G" is the sum over all edges "uv" of "G" of number of edges which are not equidistant from "u" and "v".Let "G" be a graph and "e" = "uv" an edge of "G".Here formula_1 denotes the number of edges lying closer to the vertex "u" than the vertex "v", and formula_2 is the number of edges lying closer to the vertex "v" than the vertex "u".