Abstract
The zeroth-order general Randic index (usually denoted by R-0(alpha)) and variable sum exdeg index (denoted by SEI alpha) of a graph G are defined as R-0(alpha)(G) = Sigma(v is an element of V (G))(dv)(alpha) and SEI alpha(G) = Sigma(dv)(v is an element of V (G))a(dv), respectively, where d(v) is degree of the vertex v is an element of V (G), a is a positive real number different from 1 and a is a real number other than 0 and 1. A segment of a tree is a path P, whose terminal vertices are branching or/and pendent, and all non-terminal vertices (if exist) of P have degree 2. For n >= 6, let PTn, n1, STn, k, BTn, b be the collections of all n-vertex trees having n1 pendent vertices, k segments, b branching vertices, respectively. In this paper, all the trees with extremum (maximum and minimum) zeroth-order general Randic index and variable sum exdeg index are determined from the collections PTn, n1, STn, k, BTn, b. The obtained extremal trees for the collection STn, k are also extremal trees for the collection of all n-vertex trees having fixed number of vertices with degree 2 (because the number of segments of a tree T can be determined from the number of vertices of T having degree 2 and vice versa).