sufficient conditions on the zeroth-order general randic index for maximally edge-connected digraphs

Let d be a finite and simple digraph with vertex set v (d). for a vertex v∈v(d), the degree of v, denoted by d(v), is defined as the minimum value of its out-degree d+(v) and its in-degree d−(v). now let d be a digraph with minimum degree δ≥1 and edge-connectivity λ. if α is real number, then, analogously to graphs, we define the zeroth-order general randi'{c} index by ∑x∈v(d)(d(x))α. a digraph is maximally edge- connected if λ=δ. in this paper, we present sufficient conditions for digraphs to be maximally edge- connected in terms of the zeroth-order general randi'{c} index, the order and the minimum degree when α<0, 0<α<1 or 1<α≤2. using the associated digraph of a graph, we show that our results include some corresponding known results on graphs.