Connected (n,m)(n,m)-graphs with minimum and maximum zeroth-order general Randić index

Let G   be a graph and d(v)d(v) denote the degree of a vertex vv in G  . Then the zeroth-order general Randić index Rα0(G) of the graph G   is defined as ∑v∈V(G)d(v)α∑v∈V(G)d(v)α, where αα is a pertinently chosen real number. We characterize, for any αα, the connected (n,m)(n,m)-graphs with minimum and maximum Rα0.