The PI Index of polyomino chains

AbstractThe PI index is a graph invariant defined as the summation of the sums of neu(e|G) and nev(e|G) over all the edges e=uv of a connected graph G, i.e., PI(G)=∑e∈E(G)[neu(e|G)+nev(e|G)], where neu(e|G) is the number of edges of G lying closer to u than to v and nev(e|G) is the number of edges of G lying closer to v than to u. An efficient formula for calculating the PI index of polyomino chains is given, and the bounds for the PI index of polyomino chains are established