Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs
The hyper-Zagreb index is an important branch in the Zagreb indices family, which is defined as ∑uv∈E(G)(d(u)+d(v))2, where d(v) is the degree of the vertex v in a graph G=(V(G),E(G)). In this paper, the monotonicity of the hyper-Zagreb index under some graph transformations was studied. Using thes...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/6079450 |
| Summary: | The hyper-Zagreb index is an important branch in the Zagreb indices family, which is defined as ∑uv∈E(G)(d(u)+d(v))2, where d(v) is the degree of the vertex v in a graph G=(V(G),E(G)). In this paper, the monotonicity of the hyper-Zagreb index under some graph transformations was studied. Using these nice mathematical properties, the extremal graphs among n-vertex trees (acyclic), unicyclic, and bicyclic graphs are determined for hyper-Zagreb index. Furthermore, the sharp upper and lower bounds on the hyper-Zagreb index of these graphs are provided. |
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| ISSN: | 1026-0226 1607-887X |