Abstract
The general sum-connectivity index is a molecular descriptor introduced within the field of mathematical chemistry about a decade ago. For an arbitrary real number alpha, the general sum-connectivity index of a graph G is denoted chi(alpha)(G) and is defined as the sum of the numbers (d(u) + d(v))(alpha) over all edges uv of G, where d(u) and d(v) denote the degrees of the vertices u and v, respectively. This paper characterizes the trees attaining the extremum values of chi(alpha) over the class of all trees of order n and maximum degree Delta for alpha < 0 as well as for alpha > 1, where 3 <= left perpendicular n/2 right perpendicular <= Delta <= n - 2.