Graphs with fixed number of pendent vertices and minimal Zeroth-order general Randić index

We investigate the graph with minimal Zeroth-order general Randić index in terms of its order n, pendent number N1 and cyclomatic number γ   ≥ 0. Extremal graphs were completely characterized for cases of γ=0,1,2,γ=0,1,2, which can be directly extended for graphs with cyclomatic number γ ≥ 3.