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

#### Abstract

*H*

_{f}(

*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.

#### Keywords

#### Full Text:

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

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