On the first Zagreb index and multiplicative Zagreb coindices of graphs
For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as , where dG(vi) is the degree of vertex vi in G. Recently Xu et al. introduced two graphical invariants and named as first multiplicative Zagreb coindex and second multiplicative Zagreb coin...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2016-01-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/auom-2016-0008 |
| _version_ | 1811329843829145600 |
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| author | Das Kinkar Ch. Akgunes Nihat Togan Muge Yurttas Aysun Cangul I. Naci Cevik A. Sinan |
| author_facet | Das Kinkar Ch. Akgunes Nihat Togan Muge Yurttas Aysun Cangul I. Naci Cevik A. Sinan |
| author_sort | Das Kinkar Ch. |
| collection | DOAJ |
| description | For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as , where dG(vi) is the degree of vertex vi in G. Recently Xu et al. introduced two graphical invariants and named as first multiplicative Zagreb coindex and second multiplicative Zagreb coindex, respectively. The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G, that is, NK(G) = . The irregularity index t(G) of G is defined as the number of distinct terms in the degree sequence of G. In this paper, we give some lower and upper bounds on the first Zagreb index M1(G) of graphs and trees in terms of number of vertices, irregularity index, maxi- mum degree, and characterize the extremal graphs. Moreover, we obtain some lower and upper bounds on the (first and second) multiplicative Zagreb coindices of graphs and characterize the extremal graphs. Finally, we present some relations between first Zagreb index and Narumi-Katayama index, and (first and second) multiplicative Zagreb index and coindices of graphs. |
| first_indexed | 2024-04-13T15:51:11Z |
| format | Article |
| id | doaj.art-9adf6e5f52d24607aa1e9cb2902d07c5 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-13T15:51:11Z |
| publishDate | 2016-01-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-9adf6e5f52d24607aa1e9cb2902d07c52022-12-22T02:40:50ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352016-01-0124115317610.1515/auom-2016-0008On the first Zagreb index and multiplicative Zagreb coindices of graphsDas Kinkar Ch.0Akgunes Nihat1Togan Muge2Yurttas Aysun3Cangul I. Naci4Cevik A. Sinan5Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of KoreaDepartment of Mathematics-Computer Sciences, Necmettin Erbakan University, Faculty of Science, Meram Yeniyol, 42100, Konya, TurkeyDepartment of Mathematics, Uludag University, Faculty of Science and Art, Gorukle Campus, 16059, Bursa, TurkeyDepartment of Mathematics, Uludag University, Faculty of Science and Art, Gorukle Campus, 16059, Bursa, TurkeyDepartment of Mathematics, Uludag University, Faculty of Science and Art, Gorukle Campus, 16059, Bursa, TurkeyDepartment of Mathematics, Selcuk University, Faculty of Science, Campus, 42075, Konya, TurkeyFor a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as , where dG(vi) is the degree of vertex vi in G. Recently Xu et al. introduced two graphical invariants and named as first multiplicative Zagreb coindex and second multiplicative Zagreb coindex, respectively. The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G, that is, NK(G) = . The irregularity index t(G) of G is defined as the number of distinct terms in the degree sequence of G. In this paper, we give some lower and upper bounds on the first Zagreb index M1(G) of graphs and trees in terms of number of vertices, irregularity index, maxi- mum degree, and characterize the extremal graphs. Moreover, we obtain some lower and upper bounds on the (first and second) multiplicative Zagreb coindices of graphs and characterize the extremal graphs. Finally, we present some relations between first Zagreb index and Narumi-Katayama index, and (first and second) multiplicative Zagreb index and coindices of graphs.https://doi.org/10.1515/auom-2016-0008first zagreb indexfirst and second multiplicative zagreb coindexnarumi-katayama indexprimary 05c07secondary 05c12 |
| spellingShingle | Das Kinkar Ch. Akgunes Nihat Togan Muge Yurttas Aysun Cangul I. Naci Cevik A. Sinan On the first Zagreb index and multiplicative Zagreb coindices of graphs Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica first zagreb index first and second multiplicative zagreb coindex narumi-katayama index primary 05c07 secondary 05c12 |
| title | On the first Zagreb index and multiplicative Zagreb coindices of graphs |
| title_full | On the first Zagreb index and multiplicative Zagreb coindices of graphs |
| title_fullStr | On the first Zagreb index and multiplicative Zagreb coindices of graphs |
| title_full_unstemmed | On the first Zagreb index and multiplicative Zagreb coindices of graphs |
| title_short | On the first Zagreb index and multiplicative Zagreb coindices of graphs |
| title_sort | on the first zagreb index and multiplicative zagreb coindices of graphs |
| topic | first zagreb index first and second multiplicative zagreb coindex narumi-katayama index primary 05c07 secondary 05c12 |
| url | https://doi.org/10.1515/auom-2016-0008 |
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