On the first Zagreb index of graphs with Self-Loops
AbstractSome of the most comprehensively studied degree-based topological indices are the Zagreb indices. The first Zagreb index [Formula: see text] of a graph G is defined as the sum of squares of the degrees of the vertices. Let [Formula: see text] and let [Formula: see text] be the graph obtained...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2023-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2023.2246515 |
| _version_ | 1797385655084384256 |
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| author | Shashwath S. Shetty Arathi Bhat K |
| author_facet | Shashwath S. Shetty Arathi Bhat K |
| author_sort | Shashwath S. Shetty |
| collection | DOAJ |
| description | AbstractSome of the most comprehensively studied degree-based topological indices are the Zagreb indices. The first Zagreb index [Formula: see text] of a graph G is defined as the sum of squares of the degrees of the vertices. Let [Formula: see text] and let [Formula: see text] be the graph obtained from the simple graph G, by attaching a self-loop to each of its vertices belonging to X. In this article, some sharp bounds for the first Zagreb index of graphs with self-loops using various parameters has been put forward. |
| first_indexed | 2024-03-08T21:57:25Z |
| format | Article |
| id | doaj.art-bcc8c712ae354b9e96278c79a41d7967 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 2543-3474 |
| language | English |
| last_indexed | 2024-03-08T21:57:25Z |
| publishDate | 2023-09-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-bcc8c712ae354b9e96278c79a41d79672023-12-19T17:41:02ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742023-09-0120332633110.1080/09728600.2023.2246515On the first Zagreb index of graphs with Self-LoopsShashwath S. Shetty0Arathi Bhat K1Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, IndiaDepartment of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, IndiaAbstractSome of the most comprehensively studied degree-based topological indices are the Zagreb indices. The first Zagreb index [Formula: see text] of a graph G is defined as the sum of squares of the degrees of the vertices. Let [Formula: see text] and let [Formula: see text] be the graph obtained from the simple graph G, by attaching a self-loop to each of its vertices belonging to X. In this article, some sharp bounds for the first Zagreb index of graphs with self-loops using various parameters has been put forward.https://www.tandfonline.com/doi/10.1080/09728600.2023.2246515Zagreb indexgraph with self-loopssum of squares of the degreesNordhaus-Gaddum type of bound05C9205C35 |
| spellingShingle | Shashwath S. Shetty Arathi Bhat K On the first Zagreb index of graphs with Self-Loops AKCE International Journal of Graphs and Combinatorics Zagreb index graph with self-loops sum of squares of the degrees Nordhaus-Gaddum type of bound 05C92 05C35 |
| title | On the first Zagreb index of graphs with Self-Loops |
| title_full | On the first Zagreb index of graphs with Self-Loops |
| title_fullStr | On the first Zagreb index of graphs with Self-Loops |
| title_full_unstemmed | On the first Zagreb index of graphs with Self-Loops |
| title_short | On the first Zagreb index of graphs with Self-Loops |
| title_sort | on the first zagreb index of graphs with self loops |
| topic | Zagreb index graph with self-loops sum of squares of the degrees Nordhaus-Gaddum type of bound 05C92 05C35 |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2023.2246515 |
| work_keys_str_mv | AT shashwathsshetty onthefirstzagrebindexofgraphswithselfloops AT arathibhatk onthefirstzagrebindexofgraphswithselfloops |