The Sombor index and coindex of two-trees
The Sombor index of a graph $ G $, introduced by Ivan Gutman, is defined as the sum of the weights $ \sqrt{d_G(u)^2+d_G(v)^2} $ of all edges $ uv $ of $ G $, where $ d_G(u) $ denotes the degree of vertex $ u $ in $ G $. The Sombor coindex was recently defined as $ \overline{SO}(G) = \sum_{uv\notin E...
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AIMS Press
2023-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023967?viewType=HTML |
| _version_ | 1797801092035117056 |
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| author | Zenan Du Lihua You Hechao Liu Yufei Huang |
| author_facet | Zenan Du Lihua You Hechao Liu Yufei Huang |
| author_sort | Zenan Du |
| collection | DOAJ |
| description | The Sombor index of a graph $ G $, introduced by Ivan Gutman, is defined as the sum of the weights $ \sqrt{d_G(u)^2+d_G(v)^2} $ of all edges $ uv $ of $ G $, where $ d_G(u) $ denotes the degree of vertex $ u $ in $ G $. The Sombor coindex was recently defined as $ \overline{SO}(G) = \sum_{uv\notin E(G)}\sqrt{d_G(u)^2+d_G(v)^2} $. As a new vertex-degree-based topological index, the Sombor index is important because it has been proved to predict certain physicochemical properties. Two-trees are very important structures in complex networks. In this paper, the maximum and second maximum Sombor index, the minimum and second minimum Sombor coindex of two-trees and the extremal two-trees are determined, respectively. Besides, some problems are proposed for further research. |
| first_indexed | 2024-03-13T04:45:10Z |
| format | Article |
| id | doaj.art-2f3b1af2033e4a3aaee99888f2965e8f |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-13T04:45:10Z |
| publishDate | 2023-06-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj.art-2f3b1af2033e4a3aaee99888f2965e8f2023-06-19T01:20:41ZengAIMS PressAIMS Mathematics2473-69882023-06-0188189821899410.3934/math.2023967The Sombor index and coindex of two-treesZenan Du 0Lihua You 1Hechao Liu2Yufei Huang31. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China2. Department of Mathematics Teaching, Guangzhou Civil Aviation College, Guangzhou 510403, ChinaThe Sombor index of a graph $ G $, introduced by Ivan Gutman, is defined as the sum of the weights $ \sqrt{d_G(u)^2+d_G(v)^2} $ of all edges $ uv $ of $ G $, where $ d_G(u) $ denotes the degree of vertex $ u $ in $ G $. The Sombor coindex was recently defined as $ \overline{SO}(G) = \sum_{uv\notin E(G)}\sqrt{d_G(u)^2+d_G(v)^2} $. As a new vertex-degree-based topological index, the Sombor index is important because it has been proved to predict certain physicochemical properties. Two-trees are very important structures in complex networks. In this paper, the maximum and second maximum Sombor index, the minimum and second minimum Sombor coindex of two-trees and the extremal two-trees are determined, respectively. Besides, some problems are proposed for further research.https://www.aimspress.com/article/doi/10.3934/math.2023967?viewType=HTMLsombor indexsombor coindextwo-tree |
| spellingShingle | Zenan Du Lihua You Hechao Liu Yufei Huang The Sombor index and coindex of two-trees AIMS Mathematics sombor index sombor coindex two-tree |
| title | The Sombor index and coindex of two-trees |
| title_full | The Sombor index and coindex of two-trees |
| title_fullStr | The Sombor index and coindex of two-trees |
| title_full_unstemmed | The Sombor index and coindex of two-trees |
| title_short | The Sombor index and coindex of two-trees |
| title_sort | sombor index and coindex of two trees |
| topic | sombor index sombor coindex two-tree |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023967?viewType=HTML |
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