Abstract

In this paper, we show that in the class of connected unicyclic graphs G of order n≥3 having 0≤k≤n−3 pendant vertices, the unique graph G having minimum general sum-connectivity index χα(G) consists of Cn−k and k pendant vertices adjacent to a unique vertex of Cn−k, if −1≤α<0. This property does not hold for zeroth-order general Randić index 0Rα(G).

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