Some Upper Bounds on the First General Zagreb Index
The first general Zagreb index MγG or zeroth-order general Randić index of a graph G is defined as MγG=∑v∈Vdvγ where γ is any nonzero real number, dv is the degree of the vertex v and γ=2 gives the classical first Zagreb index. The researchers investigated some sharp upper and lower bounds on zeroth...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/8131346 |
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| author | Muhammad Kamran Jamil Aisha Javed Ebenezer Bonyah Iqra Zaman |
| author_facet | Muhammad Kamran Jamil Aisha Javed Ebenezer Bonyah Iqra Zaman |
| author_sort | Muhammad Kamran Jamil |
| collection | DOAJ |
| description | The first general Zagreb index MγG or zeroth-order general Randić index of a graph G is defined as MγG=∑v∈Vdvγ where γ is any nonzero real number, dv is the degree of the vertex v and γ=2 gives the classical first Zagreb index. The researchers investigated some sharp upper and lower bounds on zeroth-order general Randić index (for γ<0) in terms of connectivity, minimum degree, and independent number. In this paper, we put sharp upper bounds on the first general Zagreb index in terms of independent number, minimum degree, and connectivity for γ. Furthermore, extremal graphs are also investigated which attained the upper bounds. |
| format | Article |
| id | doaj-art-ceb60d028c3b421dac2d71148e732687 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ceb60d028c3b421dac2d71148e7326872025-02-03T06:11:18ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/8131346Some Upper Bounds on the First General Zagreb IndexMuhammad Kamran Jamil0Aisha Javed1Ebenezer Bonyah2Iqra Zaman3Department of MathematicsAbdus Salam School of Mathematical SciencesDepartment of Mathematics EducationDepartment of MathematicsThe first general Zagreb index MγG or zeroth-order general Randić index of a graph G is defined as MγG=∑v∈Vdvγ where γ is any nonzero real number, dv is the degree of the vertex v and γ=2 gives the classical first Zagreb index. The researchers investigated some sharp upper and lower bounds on zeroth-order general Randić index (for γ<0) in terms of connectivity, minimum degree, and independent number. In this paper, we put sharp upper bounds on the first general Zagreb index in terms of independent number, minimum degree, and connectivity for γ. Furthermore, extremal graphs are also investigated which attained the upper bounds.http://dx.doi.org/10.1155/2022/8131346 |
| spellingShingle | Muhammad Kamran Jamil Aisha Javed Ebenezer Bonyah Iqra Zaman Some Upper Bounds on the First General Zagreb Index Journal of Mathematics |
| title | Some Upper Bounds on the First General Zagreb Index |
| title_full | Some Upper Bounds on the First General Zagreb Index |
| title_fullStr | Some Upper Bounds on the First General Zagreb Index |
| title_full_unstemmed | Some Upper Bounds on the First General Zagreb Index |
| title_short | Some Upper Bounds on the First General Zagreb Index |
| title_sort | some upper bounds on the first general zagreb index |
| url | http://dx.doi.org/10.1155/2022/8131346 |
| work_keys_str_mv | AT muhammadkamranjamil someupperboundsonthefirstgeneralzagrebindex AT aishajaved someupperboundsonthefirstgeneralzagrebindex AT ebenezerbonyah someupperboundsonthefirstgeneralzagrebindex AT iqrazaman someupperboundsonthefirstgeneralzagrebindex |