Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number
The zeroth-order general Randić index of graph $ G = (V_G, E_G) $, denoted by $ ^0R_{\alpha}(G) $, is the sum of items $ (d_{v})^{\alpha} $ over all vertices $ v\in V_G $, where $ \alpha $ is a pertinently chosen real number. In this paper, we obtain the sharp upper and lower bounds on $ ^0R_{\alpha...
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AIMS Press
2022-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022142?viewType=HTML |
| _version_ | 1819283441690083328 |
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| author | Chang Liu Jianping Li |
| author_facet | Chang Liu Jianping Li |
| author_sort | Chang Liu |
| collection | DOAJ |
| description | The zeroth-order general Randić index of graph $ G = (V_G, E_G) $, denoted by $ ^0R_{\alpha}(G) $, is the sum of items $ (d_{v})^{\alpha} $ over all vertices $ v\in V_G $, where $ \alpha $ is a pertinently chosen real number. In this paper, we obtain the sharp upper and lower bounds on $ ^0R_{\alpha} $ of trees with a given domination number $ \gamma $, for $ \alpha\in(-\infty, 0)\cup(1, \infty) $ and $ \alpha\in(0, 1) $, respectively. The corresponding extremal graphs of these bounds are also characterized. |
| first_indexed | 2024-12-24T01:31:32Z |
| format | Article |
| id | doaj.art-e0817bd851e64b5fabdecf1c59cec940 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-24T01:31:32Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-e0817bd851e64b5fabdecf1c59cec9402022-12-21T17:22:21ZengAIMS PressAIMS Mathematics2473-69882022-01-01722529254210.3934/math.2022142Sharp bounds on the zeroth-order general Randić index of trees in terms of domination numberChang Liu 0Jianping Li 1College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, ChinaCollege of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, ChinaThe zeroth-order general Randić index of graph $ G = (V_G, E_G) $, denoted by $ ^0R_{\alpha}(G) $, is the sum of items $ (d_{v})^{\alpha} $ over all vertices $ v\in V_G $, where $ \alpha $ is a pertinently chosen real number. In this paper, we obtain the sharp upper and lower bounds on $ ^0R_{\alpha} $ of trees with a given domination number $ \gamma $, for $ \alpha\in(-\infty, 0)\cup(1, \infty) $ and $ \alpha\in(0, 1) $, respectively. The corresponding extremal graphs of these bounds are also characterized.https://www.aimspress.com/article/doi/10.3934/math.2022142?viewType=HTMLthe zeroth-order general randić indexextremal treesdomination number |
| spellingShingle | Chang Liu Jianping Li Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number AIMS Mathematics the zeroth-order general randić index extremal trees domination number |
| title | Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number |
| title_full | Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number |
| title_fullStr | Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number |
| title_full_unstemmed | Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number |
| title_short | Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number |
| title_sort | sharp bounds on the zeroth order general randic index of trees in terms of domination number |
| topic | the zeroth-order general randić index extremal trees domination number |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022142?viewType=HTML |
| work_keys_str_mv | AT changliu sharpboundsonthezerothordergeneralrandicindexoftreesintermsofdominationnumber AT jianpingli sharpboundsonthezerothordergeneralrandicindexoftreesintermsofdominationnumber |