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Abstract-A tree T is labeled when the n vertices are distinguished from one another by names such as v 1 , v 2 , , v n . Two labeled trees are considered to be distinct if they have different vertex labels even though they might be isomorphic. According to Cayley's tree formula, there are n n-2 labeled trees on n vertices. Prüfer used a simple way to prove this formula and demonstrated that there exists a mapping between a labeled tree and a number sequence. From his proof, we can find a naive sequential algorithm which transfers a labeled tree to a number sequence and vice versa. However, it is hard to parallelize. In this paper, we shall propose an O(log n) time parallel algorithm for constructing a labeled tree by using O(n) processors and O(n log n) space on the EREW PRAM computational model.

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