Extremal quasi-unicyclic graphs with respect to vertex-degree function index

In this paper, the vertex-degree function index Hf (G) is considered when function f (x) belongs to four classes of functions determined by the following properties: strictly convex versus strictly concave and strictly increasing versus strictly decreasing. Quasi-unicyclic graphs of given order (or of given order and fixed number of pendant vertices) extremal relatively to vertex-degree func-tion index for these classes of functions are determined. These conditions are fulfilled by several topological indices of graphs.