On the general sum-connectivity index of connected graphs with given order and girth - Ioan Tomescu (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 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 Randić index ^0R_α(G).