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We give a new and short proof of a theorem on k-hypertournament losing scores due to Zhou et al. [8].

- S Pirzada, T A Naikoo
- 2006

The set S of distinct scores (outdegrees) of the vertices of a k-partite tournament T(X1, X2, · · · , X k) is called its score set. In this paper, we prove that every set of n non-negative integers, except {0} and {0, 1}, is a score set of some 3-partite tournament. We also prove that every set of n non-negative integers is a score set of some k-partite… (More)

- S Pirzada, T A Naikoo, F A Dar
- 2008

The set D of distinct signed degrees of the vertices in a signed graph G is called its signed degree set. In this paper, we prove that every non-empty set of positive (negative) integers is the signed degree set of some connected signed graph and determine the smallest possible order for such a signed graph. We also prove that every non-empty set of… (More)

- Koko K. Kayibi, Muhammad Ali Khan, Shariefuddin Pirzada, Antal Iványi, K. K. Kayibi, M. A. Khan +2 others
- 2012

The imbalance of a vertex v in a digraph D is defined as a(v) = d + (v)−d − (v), where d + (v) and d − (v) respectively denote the out-degree and indegree of vertex v. The imbalance sequence of D is formed by listing vertex imbalances in nondecreasing order. We define a minimally cyclic digraph as a connected digraph which is either acyclic or has exactly… (More)

- S. Pirzada, T. A. Naikoo
- 2008

The score of a vertex v in an oriented graph D is av = n−1+d + v −d − v , where d + v and d − v are the outdegree and indegree respectively of v and n is the number of vertices in D. The set of distinct scores of the vertices in an oriented graph D is called its score set. If a > 0 and d > 1 are positive integers, we show there exists an oriented graph with… (More)

An oriented graph is a digraph with no symmetric pairs of directed arcs and without loops.

- S. Pirzada
- 2004

We characterize irreducible score sequences of oriented graphs and give a condition for a score sequence to belong to exactly one oriented graph.

- S Pirzada, T A Naikoo, F A Dar
- 2006

A signed bipartite graph G(U, V) is a bipartite graph in which each edge is assigned a positive or a negative sign. The signed degree of a vertex x in G(U, V) is the number of positive edges incident with x less the number of negative edges incident with x. The set S of distinct signed degrees of the vertices of G(U, V) is called its signed degree set. In… (More)

Given non-negative integers n i and α i with 0 ≤ α i ≤ n i