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

Zhaoyang Luo and Jianliang Wu

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/241712

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:241712

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