Zagreb Eccentricity Indices of the Generalized Hierarchical Product Graphs and Their Applications

Let G be a connected graph. The first and second Zagreb eccentricity indices of G are defined as M1*(G)=∑v∈V(G)εG2(v) and M2*(G)=∑uv∈E(G)εG(u)εG(v), where εG(v) is the eccentricity of the vertex v in G and εG2(v)=(εG(v))2. Suppose that G(U)⊓H(∅≠U⊆V(G)) is the generalized hierarchical product of two connected graphs G and H. In this paper, the Zagreb eccentricity indices M1* and M2* of G(U)⊓H are computed. Moreover, we present explicit formulas for the M1* and M2* of S-sum graph, Cartesian, cluster, and corona product graphs by means of some invariants of the factors