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

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  • Zhaoyang Luo
  • Jianliang Wu

Abstract

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.

Suggested Citation

  • Zhaoyang Luo & Jianliang Wu, 2014. "Zagreb Eccentricity Indices of the Generalized Hierarchical Product Graphs and Their Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:241712
    DOI: 10.1155/2014/241712
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