Zagreb Eccentricity Indices of the Generalized Hierarchical Product Graphs and Their Applications. (10th February 2014) - Luo, Zhaoyang; Wu, Jianliang
Abstract : Let G be a connected graph. The first and second Zagreb eccentricity indices of G are defined as M 1 * ( G ) = ∑ v ∈ V ( G ) ‍ ε G 2 ( v ) and M 2 * ( G ) = ∑ u v ∈ E ( G ) ‍ ε G ( u ) ε G ( v ), where ε G ( v ) is the eccentricity of the vertex v in G and ε G 2 ( v ) = ( ε G ( 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 M 1 * and M 2 * of G ( U ) ⊓ 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.