Sharp bounds on the zeroth-order general Randić index of unicyclic graphs with given diameter

Let G be a simple connected graph and α be a given real number. The zeroth-order general Randić index 0Rα(G) is defined as ∑v∈V(G)[dG(v)]α, where dG(v) denotes the degree of the vertex v of G. In this work, we give, for any α(≠0,1), some sharp bounds on the zeroth-order general Randić index 0Rα of all unicyclic graphs with n vertices and diameter d.