Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21281120160601Sufficient conditions on the zeroth-order general Randic index for maximally edge-connected digraphs1131351410.22049/cco.2016.13514ENLutzVolkmannRWTH Aachen University0000-0003-3496-277XJournal Article20151120Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $vin V(D)$, 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 $deltage 1$ and edge-connectivity $lambda$. If $alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi'{c} index by $sum_{xin V(D)}(d(x))^{alpha}$. A digraph is maximally edge-connected if $lambda=delta$. 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 $alpha <0$, $0<alpha <1$ or $1<alphale 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs. http://comb-opt.azaruniv.ac.ir/article_13514_2c29013911bbc87b1dc4be81c6823349.pdf