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A problem to make a graph strongly connected is one of the most fundamental problems in graph theory. The known parallel algorithm solves this problem in O(log n) time using O(n3) processors on a CRCW PRAM model. In this paper we present a parallel algorithm to find the minimum edges to make a disconnected directed acyclic graph strongly connected in O(log(m + n)) time using O(m + n) processors on a CREW PRAM model. This algorithm is an efficient parallel algorithm because the number of processors varies according to the density of the given graph.