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

Ioan Tomescu


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.


quasi-unicyclic graphs, vertex-degree function index , strictly convex/strictly concave function, strictly increasing/strictly decreasing function, Jensen inequality

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DOI: http://dx.doi.org/10.5614/ejgta.2023.11.1.4


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