Vertex and edge Padmakar-Ivan indices of the generalized hierarchical product of graphs

The vertex Padmakar-Ivan index of a graph G, denoted by PIv (G), is the sum over all edges uv of G of the number of vertices which are not equidistant from u and v. Similarly, edge Padmakar-Ivan index of a graph G, denoted by PIe(G), is the sum over all edges uv of G of the number of edges which are not equidistant from u and v. In this paper, PIv and PIe of the generalized hierarchical product of two connected graphs are obtained. Using the results obtained here, some known results are deduced as corollaries. Finally, we obtain the PI, and PIe of the zig-zag polyhex nanotube TUHC6[2n, 2] and hexagonal chain L-n. (C) 2012 Elsevier B.V. All rights reserved.