Extermal forgotten topological index of quasi-unicyclic graphs. (English) Zbl 1487.05060

Summary: The forgotten topological index of a graph \(\mathcal{G} \), denoted by \(F(\mathcal{G})\), is defined as the sum of weights \(d (u)^2+d (v)^2\) overall edges \(uv\) of \(\mathcal{G} \), where \(d(u)\) denotes the degree of a vertex \(u\). The graph \(\mathcal{G}\) is called a quasi-unicyclic graph if there exists a vertex \(v\in\mathcal{V}(\mathcal{G})\) such that \(\mathcal{G}-v\) is a connected graph with a unique cycle. In this paper, we give sharp upper and lower bounds for the F-index (forgotten topological index) of the quasi-unicyclic graphs.


05C09 Graphical indices (Wiener index, Zagreb index, Randić index, etc.)
05C07 Vertex degrees
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