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 ∈ V deg α ( 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 ] ). [ABSTRACT FROM AUTHOR]