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...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/6079450 |
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| author | Wei Gao Muhammad Kamran Jamil Aisha Javed Mohammad Reza Farahani Shaohui Wang Jia-Bao Liu |
| author_facet | Wei Gao Muhammad Kamran Jamil Aisha Javed Mohammad Reza Farahani Shaohui Wang Jia-Bao Liu |
| author_sort | Wei Gao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8a14e942171342528621223e3fcdda01 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8a14e942171342528621223e3fcdda012025-02-03T01:23:20ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/60794506079450Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic GraphsWei Gao0Muhammad Kamran Jamil1Aisha Javed2Mohammad Reza Farahani3Shaohui Wang4Jia-Bao Liu5School of Information Science and Technology, Yunnan Normal University, Kunming 650500, ChinaRiphah Institute of Computing and Applied Sciences (RICAS), Riphah International University, Lahore, PakistanAbdus Salam School of Mathematical Sciences, Government College University, Lahore, PakistanDepartment of Applied Mathematics, Iran University of Science and Technology, Narmak, Tehran, IranDepartment of Mathematics and Computer Science, Adelphi University, Garden City, NY 11530, USASchool of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaThe 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.http://dx.doi.org/10.1155/2017/6079450 |
| spellingShingle | Wei Gao Muhammad Kamran Jamil Aisha Javed Mohammad Reza Farahani Shaohui Wang Jia-Bao Liu Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs Discrete Dynamics in Nature and Society |
| title | Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs |
| title_full | Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs |
| title_fullStr | Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs |
| title_full_unstemmed | Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs |
| title_short | Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs |
| title_sort | sharp bounds of the hyper zagreb index on acyclic unicylic and bicyclic graphs |
| url | http://dx.doi.org/10.1155/2017/6079450 |
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