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 \(\left(d(u) + d(v)\right)^{\alpha}\) 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 \(3 \leq \left\lceil n/2\right\rceil \leq \Delta \leq n-2\).