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 tw...
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/241712 |
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| author | Zhaoyang Luo Jianliang Wu |
| author_facet | Zhaoyang Luo Jianliang Wu |
| author_sort | Zhaoyang Luo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e252c8005b4944a094f3ae479385c569 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e252c8005b4944a094f3ae479385c5692025-02-03T05:47:52ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/241712241712Zagreb Eccentricity Indices of the Generalized Hierarchical Product Graphs and Their ApplicationsZhaoyang Luo0Jianliang Wu1School of Mathematics, Shandong University, Jinan 250100, ChinaSchool of Mathematics, Shandong University, Jinan 250100, ChinaLet 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.http://dx.doi.org/10.1155/2014/241712 |
| spellingShingle | Zhaoyang Luo Jianliang Wu Zagreb Eccentricity Indices of the Generalized Hierarchical Product Graphs and Their Applications Journal of Applied Mathematics |
| title | Zagreb Eccentricity Indices of the Generalized Hierarchical Product Graphs and Their Applications |
| title_full | Zagreb Eccentricity Indices of the Generalized Hierarchical Product Graphs and Their Applications |
| title_fullStr | Zagreb Eccentricity Indices of the Generalized Hierarchical Product Graphs and Their Applications |
| title_full_unstemmed | Zagreb Eccentricity Indices of the Generalized Hierarchical Product Graphs and Their Applications |
| title_short | Zagreb Eccentricity Indices of the Generalized Hierarchical Product Graphs and Their Applications |
| title_sort | zagreb eccentricity indices of the generalized hierarchical product graphs and their applications |
| url | http://dx.doi.org/10.1155/2014/241712 |
| work_keys_str_mv | AT zhaoyangluo zagrebeccentricityindicesofthegeneralizedhierarchicalproductgraphsandtheirapplications AT jianliangwu zagrebeccentricityindicesofthegeneralizedhierarchicalproductgraphsandtheirapplications |