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

Ioan Tomescu (University of Bucharest)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 11, No 1 (2023): Electronic Journal of Graph Theory and Applications

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 function index for these classes of functions are determined. These conditions are fulfilled by several topological indices of graphs.