Extremal Degree-Ratio Sombor Index Trees

Abstract:

The Sombor index is a geometry-motivated vertex-degree-based graph invariant, defined as the sum of the terms √(d(u)²+d(v)²) over all pairs of adjacent vertices; d(u) is the degree of the vertex u. Recently, Nyauli and Buragohain introduced a novel, “degree-ratio” variant of the Sombor index, defined via √([d(u)/d(v)]²+[d(v)/d(u)]²). In this paper, we determine the trees with maximum, second- and third-maximum, as well as minimum and second-minimum degree-ratio Sombor index.