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- Shariefuddin Pirzada, Guofei Zhou
- ArXiv
- 2010

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, +5 authors A. Iványi
- 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)

- Shariefuddin Pirzada, T. A. Naikoo, Guofei Zhou
- Graphs and Combinatorics
- 2007

- 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)

- S. Pirzada, T. A. Naikoo, T. A. Chishti
- 2006

The set A of distinct scores of the vertices of an oriented bipartite graph D(U, V) is called its score set. We consider the following question: given a finite, nonempty set A of positive integers, is there an oriented bipartite graph D(U, V) such that score set of D(U, V) is A? We conjecture that there is an affirmative answer, and verify this conjecture… (More)