Lower Bounds on the Entire Zagreb Indices of Trees
For a (molecular) graph G, the first and the second entire Zagreb indices are defined by the formulas M1εG=∑x∈VG∪EGdx2 and M2εG=∑x is either adjacent or incident to ydxdy in which dx represents the degree of a vertex or an edge x. In the current manuscript, we establish some lower bounds on the firs...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/8616725 |
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| _version_ | 1832547101212409856 |
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| author | Liang Luo Nasrin Dehgardi Asfand Fahad |
| author_facet | Liang Luo Nasrin Dehgardi Asfand Fahad |
| author_sort | Liang Luo |
| collection | DOAJ |
| description | For a (molecular) graph G, the first and the second entire Zagreb indices are defined by the formulas M1εG=∑x∈VG∪EGdx2 and M2εG=∑x is either adjacent or incident to ydxdy in which dx represents the degree of a vertex or an edge x. In the current manuscript, we establish some lower bounds on the first and the second entire Zagreb indices and determine the extremal trees which achieve these bounds. |
| format | Article |
| id | doaj-art-a6026bd22a7c462fa1edcff1b2f2c902 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a6026bd22a7c462fa1edcff1b2f2c9022025-02-03T06:46:06ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/86167258616725Lower Bounds on the Entire Zagreb Indices of TreesLiang Luo0Nasrin Dehgardi1Asfand Fahad2Key Laboratory of High Performance Ship Technology, Wuhan University of Technology, Ministry of Education, Wuhan 430070, ChinaDepartment of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, IranDepartment of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61100, PakistanFor a (molecular) graph G, the first and the second entire Zagreb indices are defined by the formulas M1εG=∑x∈VG∪EGdx2 and M2εG=∑x is either adjacent or incident to ydxdy in which dx represents the degree of a vertex or an edge x. In the current manuscript, we establish some lower bounds on the first and the second entire Zagreb indices and determine the extremal trees which achieve these bounds.http://dx.doi.org/10.1155/2020/8616725 |
| spellingShingle | Liang Luo Nasrin Dehgardi Asfand Fahad Lower Bounds on the Entire Zagreb Indices of Trees Discrete Dynamics in Nature and Society |
| title | Lower Bounds on the Entire Zagreb Indices of Trees |
| title_full | Lower Bounds on the Entire Zagreb Indices of Trees |
| title_fullStr | Lower Bounds on the Entire Zagreb Indices of Trees |
| title_full_unstemmed | Lower Bounds on the Entire Zagreb Indices of Trees |
| title_short | Lower Bounds on the Entire Zagreb Indices of Trees |
| title_sort | lower bounds on the entire zagreb indices of trees |
| url | http://dx.doi.org/10.1155/2020/8616725 |
| work_keys_str_mv | AT liangluo lowerboundsontheentirezagrebindicesoftrees AT nasrindehgardi lowerboundsontheentirezagrebindicesoftrees AT asfandfahad lowerboundsontheentirezagrebindicesoftrees |