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On the zeroth-order general Randić index of cacti. (English) Zbl 1289.05074

Summary: The zeroth-order general Randić index of a graph \(G\) is defined as \({}^0R_{\alpha }=\sum_{v\in V(G)}d(v)^{\alpha }\), where \(d(v)\) is the degree of the vertex \(v\) in \(G\) and \(\alpha \) is an arbitrary real number. In the paper, we give sharp lower and upper bounds on the zeroth-order general Randić index of cacti.

MSC:

05C07 Vertex degrees