@article{Du2023, 
author = {Zenan Du and Lihua You and Hechao Liu and Yufei Huang},
title = {The Sombor index and coindex of two-trees},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {18982-18994},
keywords = {Sombor index, Sombor coindex, two-tree},
url = {https://www.sciopen.com/article/10.3934/math.2023967},
doi = {10.3934/math.2023967},
abstract = {The Sombor index of a graph    G, introduced by Ivan Gutman, is defined as the sum of the weights              d      G        (    u          )      2        +          d      G        (    v          )      2       of all edges    u  v of    G, where        d    G    (  u  ) denotes the degree of vertex    u in    G. The Sombor coindex was recently defined as              S      O        ¯    (  G  )  =      ∑          u      v      ∉      E      (      G      )                  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.}
}