Sufficient conditions on the zeroth-order general Randic index for maximally edge-connected digraphs

Document Type: Original paper

Author

RWTH Aachen University

Abstract

Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree  and its in-degree . Now let D be a digraph with minimum degree  and edge-connectivity If  is real number, then the zeroth-order general Randic index is defined by   .  A digraph is maximally edge-connected if . In this paper we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randic index, the order and the minimum degree when  Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs.

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