The Sombor index and coindex of two-trees

Abstract

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.

Keywords

• sombor index
• sombor coindex
• two-tree