The Bounds for the First General Zagreb Index of a Graph
The first general Zagreb index of a graph $G$ is defined as the sum of the $\alpha$th powers of the vertex degrees of $G$, where $\alpha$ is a real number such that $\alpha \neq 0$ and $\alpha \neq 1$. In this note, for $\alpha > 1$, we present upper bounds involving chromatic and clique numb...
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2021-12-01
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| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/1888936 |
| _version_ | 1797350206923079680 |
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| author | Rao Li |
| author_facet | Rao Li |
| author_sort | Rao Li |
| collection | DOAJ |
| description | The first general Zagreb index of a graph $G$ is defined as the sum of the $\alpha$th powers of the vertex degrees of $G$, where $\alpha$ is a real number such that $\alpha \neq 0$ and $\alpha \neq 1$. In this note, for $\alpha > 1$, we present upper bounds involving chromatic and clique numbers for the first general Zagreb index of a graph; for an integer $\alpha \geq 2$, we present a lower bound involving the independence number for the first general Zagreb index of a graph. |
| first_indexed | 2024-03-08T12:41:21Z |
| format | Article |
| id | doaj.art-755dd411c24e4449ae836ffe64562332 |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T12:41:21Z |
| publishDate | 2021-12-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-755dd411c24e4449ae836ffe645623322024-01-21T09:28:50ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532021-12-014413213510.32323/ujma.9736711225The Bounds for the First General Zagreb Index of a GraphRao Li0University of South Carolina AikenThe first general Zagreb index of a graph $G$ is defined as the sum of the $\alpha$th powers of the vertex degrees of $G$, where $\alpha$ is a real number such that $\alpha \neq 0$ and $\alpha \neq 1$. In this note, for $\alpha > 1$, we present upper bounds involving chromatic and clique numbers for the first general Zagreb index of a graph; for an integer $\alpha \geq 2$, we present a lower bound involving the independence number for the first general Zagreb index of a graph.https://dergipark.org.tr/tr/download/article-file/1888936the first general zagreb indexthe chromatic numberthe clique number |
| spellingShingle | Rao Li The Bounds for the First General Zagreb Index of a Graph Universal Journal of Mathematics and Applications the first general zagreb index the chromatic number the clique number |
| title | The Bounds for the First General Zagreb Index of a Graph |
| title_full | The Bounds for the First General Zagreb Index of a Graph |
| title_fullStr | The Bounds for the First General Zagreb Index of a Graph |
| title_full_unstemmed | The Bounds for the First General Zagreb Index of a Graph |
| title_short | The Bounds for the First General Zagreb Index of a Graph |
| title_sort | bounds for the first general zagreb index of a graph |
| topic | the first general zagreb index the chromatic number the clique number |
| url | https://dergipark.org.tr/tr/download/article-file/1888936 |
| work_keys_str_mv | AT raoli theboundsforthefirstgeneralzagrebindexofagraph AT raoli boundsforthefirstgeneralzagrebindexofagraph |