Sufficient conditions on the zeroth-order general Randić index for maximally edge-connected graphs

Let G be a connected graph with vertex set V, minimum degree δ and edge-connectivity λ. If α is a real number, then the zeroth-order general Randić index is defined by ∑x∈Vdegα(x), where deg(x) denotes the degree of the vertex x. A graph is maximally edge-connected if λ=δ. In this paper, we present sufficient conditions for connected graphs (resp. connected triangle-free graphs) to be maximally edge-connected in terms of the zeroth-order general Randić index, the order and the minimum degree when α∈(−∞,0) or α∈(1,2] (resp. α∈[−1,0)∪(1,2]).