Extremal (n,n + 1)-graphs with respected to zeroth- order general Randić index

 A (n, n + 1)-graph G is a connected simple graph with n vertices and n + 1 edges. If dv denotes the degree of the vertex v, then the zeroth-order general Randić index $$R_\alpha^0(G)$$ of the graph G is defined as $$\sum\nolimits_{v\in V(G)}d_v^\alpha$$, where α is a real number. We characterize, for any α, the (n,n + 1)-graphs with the smallest and greatest zeroth-order general Randić index.