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 N 1 and cyclomatic number γ ≥ 0. Extremal graphs were completely characterized for cases of γ = 0 , 1 , 2 , which can be directly extended for graphs with cyclomatic number γ ≥ 3. [ABSTRACT FROM AUTHOR]