Abstract
An oriented graph is a digraph with no symmetric pairs of directed arcs and without loops. The score of a vertexv i in an oriented graph D is\(a_{v_i } \) (or simply ai)\(d_{v_i }^ - \) are the outdegree and indegree, respectively, ofv i and n is the number of vertices in D. In this paper, we give a new proof of Avery’s theorem and obtain some stronger inequalities for scores in oriented graphs. We also characterize strongly transitive oriented graphs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Avery,Score sequences of oriented graphs, J. Graph Theory 15(3) (1991), 251–257.
R. A. Brualdi and J. Shen,Landau’s inequalities for tournament scores and a short proof of a Theorem on transitive sub-tournaments, J. Graph Theory38 (2001), 244–254.
H. G. Landau,On dominance relations and the structure of animal societies: III. The condition for a score structure, Bull. Math. Biophs.15 (1953), 143–148.
E. S. Mahmoodian,A critical case method of proof in combinatorial mathematics, Bull. Iranian Math. Soc. (1978) 1L-26L.
S. Pirzada and U. Samee,Inequalities in oriented graph scores, Bull. Malaysian Math. Soc. to appear.
S. Pirzada,Simple score sequences in oriented graphs, Novi Sad J. Mathematics33(1) (2003), 25–29.
C. Thomassen,Landau’s characterization of tournament score sequences, The Theory and Applications of Graphs (Kalamazoo Michigan 1980) Wiley, New York (1981) 589–591.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pirzada, S., Naikoo, T.A. & Shah, N.A. Score sequences in oriented graphs. J. Appl. Math. Comput. 23, 257–268 (2007). https://doi.org/10.1007/BF02831973
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02831973