25 Novi Sad J. Math. Vol. 33, No. 1, 2003, 25–29 SIMPLE SCORE SEQUENCES IN ORIENTED GRAPHS S. Pirzada 1 Abstract. We characterize irreducible score sequences of oriented graphs and give a condition for a score sequence to belong to exactly one oriented graph. AMS Mathematics Subject Classification (2000): 05C Key words and phrases: oriented graphs, score sequences 1. Introduction An oriented graph is a digraph with no symmetric pairs of directed arcs and without loops. Let D be an oriented graph with the vertex set V = v 1 ,v 2 , .., v n , and let odv and idv denote the outdegree and indegree, respectively, of a vertex v. Avery [1] defined s v = n − 1+ odv − idv, 0 ≤ s v ≤ 2n − 2, as the score of vertex v and S =(s 1 ,s 2 , .., s n ) in nondecreasing order is the score sequence of D. An arc from the vertex u to the vertex v is denoted by u → v and u ∼ v or v ∼ u means neither u → v nor v → u. Avery [1] has characterized the score sequence of oriented graphs. Theorem 1.1. [1] A nondecreasing sequence of non-negative integers S =(s 1 , s 2 ,...,s n ) is the score sequence of an oriented graph if and only if for k = 1, 2,...,n k  i=1 s i ≥ K(k − 1) and equality holds for k = n. A triple in an oriented graph is an induced subdigraph with three vertices. The triples of the form u ← v, v ← w, w ← u or u ← v, u ← w, u ∼ w are called intransitive triples and the triples u ∼ v, v ∼ w, w ∼ u or u ∼ v, v ∼ w, u ← w are called transitive triples. Avery [1] gave the following results. Theorem 1.2. [1] Let D and D be two oriented graphs with the same score sequence. Then D can be transformed to D by successively transforming appro- priate triples in one of the following ways: 1 Department of Mathematics and Statistics The University of Kashmir Srinagar–190 006, Kashmir, India