On the general sum-connectivity index of connected graphs with given order and girth - Ioan Tomescu (Electronic Journal of Graph Theory and Applications (EJGTA), 2016)
In this paper, we show that in the classof connected graphs $G$ of order $n≥ 3$ having girth at least equal to $k$, $3≤ k≤ n$, the unique graph $G$ having minimum general sum-connectivity index $χ _{α }(G)$ consists of $C_{k}$ and $n-k$ pendant vertices adjacent to a unique vertex of $C_{k}$, if $-1≤ α <0$. This property does not hold for zeroth-order general Randi\' c index $^{0}R_{α}(G)$.