On the extremal Sombor index of trees with a given diameter
作者：
Highlights：
• As a new vertex-degree-based topological indices, the Sombor index studied in this paper differs from the earlier vertex-degree-based topological indices because it has a peculiar geometric interpretation.
• All the -order trees with diameter 3 are ordered with respect to the Sombor index.
• The largest and the second largest Sombor indices of -vertex trees with a given diameter are determined and the corresponding trees are characterized.
• For , we characterize the extremal -order trees which reach from the third to the fourth (resp. the sixth, the seventh) largest Sombor indices with (resp. ). For , we characterize the extremal -order trees which reach from the third to the fifth (resp. the eighth, the ninth) largest Sombor indices with (resp. ).
• As consequences, the top four -order trees with respect to the Sombor index are characterized.
摘要
•As a new vertex-degree-based topological indices, the Sombor index studied in this paper differs from the earlier vertex-degree-based topological indices because it has a peculiar geometric interpretation.•All the -order trees with diameter 3 are ordered with respect to the Sombor index.•The largest and the second largest Sombor indices of -vertex trees with a given diameter are determined and the corresponding trees are characterized.•For , we characterize the extremal -order trees which reach from the third to the fourth (resp. the sixth, the seventh) largest Sombor indices with (resp. ). For , we characterize the extremal -order trees which reach from the third to the fifth (resp. the eighth, the ninth) largest Sombor indices with (resp. ).•As consequences, the top four -order trees with respect to the Sombor index are characterized.
论文关键词：Sombor index,Tree,Diameter,Diametrical path
论文评审过程：Received 29 June 2021, Revised 20 August 2021, Accepted 5 October 2021, Available online 29 October 2021, Version of Record 29 October 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126731
