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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)

- Shariefuddin Pirzada, Ashay Dharwadker
- 2009

Graph theory is becoming increasingly significant as it is applied to other areas of mathematics, science and technology. It is being actively used in fields as varied as biochemistry (genomics), electrical engineering (communication networks and coding theory), computer science (algorithms and computation) and operations research (scheduling). The powerful… (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
- 2006

A k-digraph is an orientation of a multi-graph that is without loops and contains at most k edges between any pair of distinct vertices. We obtain necessary and sufficient conditions for a sequence of non-negative integers in non-decreasing order to be a sequence of numbers, called marks (k-scores), attached to vertices of a k-digraph. We characterize… (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)

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

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)