Score Sequences of Tournaments with Repeated Values

Authors

  • Madhukar Sharma  Department of Applied Sciences, IIMT College of Engineering, Greater Noida, Uttar Pradesh, India
  • Pawan Saxena  Department of Applied Sciences, IIMT College of Engineering, Greater Noida, Uttar Pradesh, India

Keywords:

Tournament, Score, Score Sequence.

Abstract

In this paper we define score sequences with repetitions. The strong score sequences with a single repetition of length four are characterized and the total number of strong score sequences with a single repetition is obtained. We characterize the self-converse strong score sequences with a single repetition of length three and five and report the number of self-converse strong score sequences with a single repetition. In last we conjecture a result to find the number of self-converse strong score sequences with a single repetition of order n.

References

  1. Chen G, Piotroswski W and Shreve Werren (1995), "Degree sequences with single repetitions", Congr. Numer. Vol. 106, pp. 27-32.
  2. Eplett, W J R (1979), "Self-converse tournaments", Canad. Math. Bull. Vol. 22, 23-27.
  3. Landau, H G(1953), "On dominance relations and the structure of animal societies, III: The condition for a score structure", Bull. Math. Biophysics Vol. 15, pp. 143-148.
  4. Reid, K B(1996), "Tournaments: Scores, kings, generalizations and special topics, In: Surveys on Graph Theory (edited by G. Chartrand and M. Jacobson)", Congr. Numer. Vol. 115, pp. 171-211.
  5. Ankit Garg, Arpit Goel and Amitabha Tripathi(2011), "Constructive extensions of two results on graphic sequences", Discrete Applied Mathematics Vol. 159, pp. 2170–2174
  6. mitabha Tripathi and Himanshu Tyagi (2008),  A simple criterion on degree sequences of graphs, Discrete Applied Mathematics Vol. 156, No. 18, 3513-3517.

International Journal of Scientific Research in Science, Engineering and Technology

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Published

2016-12-30

Issue

Volume 2, Issue 6, November-December-2016

Section

Research Articles

License

Copyright (c) IJSRSET

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Madhukar Sharma, Pawan Saxena "Score Sequences of Tournaments with Repeated Values" International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 2, Issue 6, pp.458-461, November-December-2016.