Total Eccentricity Index of the Generalized Hierarchical Product of Graphs

Let G = (V(G), E(G)) be a connected graph. The total eccentricity index of G is defined as ζ(G) = v∈V(G) εG(v), where εG(v) is the eccentricity of the vertex v. In this paper, we compute the total eccentricity of generalized hierarchical product of graphs. Moreover, we derive some explicit formulae for total eccentricity index of F-sum graph, Cartesian product, Cluster product and Corona product of graphs and apply those results to find the total eccentricity index of various classes of chemical graphs and nanostructures.