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 M-1*(G) = Sigma(v is an element of V(G)) epsilon(2)(G)(v) and M-2* = = Sigma(uv is an element of E(G)) epsilon(G)(u)epsilon(G)(v), where epsilon(G)(v) is the eccentricity of the vertex v in G and epsilon(2)(G)(v) - epsilon(G)(v))(2). Suppose that G(U) Pi H(empty set not equal U subset of V(G)) is the generalized hierarchical product of two connected graphs G and H. In this paper, the Zagreb eccentricity indices M-1* M-2* of G(U) Pi H are computed. Moreover, we present explicit formulas for the M-1* and M-2* of S-sum graph, Cartesian, cluster, and corona product graphs by means of some invariants of the factors.