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On Graphs of Dualities of Bipartite Posets

Year 2015, Volume: 5 Issue: 1, 29 - 30, 23.06.2015
https://doi.org/10.17678/beujst.68121

Abstract

In this paper we introduce some new graphs obtained from
bipartite posets. We show that lower-minimal graph of a bipartite poset
is isomorphic to upper-maximal graph of dual of the poset by using set
representations of the posets.


References

  • Chartrand, G. Isomorphic Graphs, Introductory Graph Theory. New York: Dover,
  • ; pp. 32-40.
  • Gratzer, G. Lattice theory: Foundation, Springer Science and Business Media;
  • , pp. 5-6.
  • Simovici, Dan A.; Djeraba C. Partially Ordered Sets. Mathematical Tools for Data
  • Mining: Set Theory, Partial Orders, Combinatorics. Springer, 2008; pp. 129-172.
  • Skiena, S. Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica ,Cambridge University Press, 2003, pp. 306-316.
  • Steiner, G.; Stewart, L. K. A linear time algorithm to find the jump number of
  • -dimensional bipartite partial orders, Order, 1987, 3(4), 359-367.
  • Civan, Y., Upper maximal graphs of posets, Order, Vol 30:2, 2013, 677-688.

Year 2015, Volume: 5 Issue: 1, 29 - 30, 23.06.2015
https://doi.org/10.17678/beujst.68121

Abstract

References

  • Chartrand, G. Isomorphic Graphs, Introductory Graph Theory. New York: Dover,
  • ; pp. 32-40.
  • Gratzer, G. Lattice theory: Foundation, Springer Science and Business Media;
  • , pp. 5-6.
  • Simovici, Dan A.; Djeraba C. Partially Ordered Sets. Mathematical Tools for Data
  • Mining: Set Theory, Partial Orders, Combinatorics. Springer, 2008; pp. 129-172.
  • Skiena, S. Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica ,Cambridge University Press, 2003, pp. 306-316.
  • Steiner, G.; Stewart, L. K. A linear time algorithm to find the jump number of
  • -dimensional bipartite partial orders, Order, 1987, 3(4), 359-367.
  • Civan, Y., Upper maximal graphs of posets, Order, Vol 30:2, 2013, 677-688.
There are 10 citations in total.

Details

Primary Language English
Authors

Selçuk Topal

Submission Date February 24, 2015
Publication Date June 23, 2015
Published in Issue Year 2015 Volume: 5 Issue: 1

Cite

IEEE S. Topal, “On Graphs of Dualities of Bipartite Posets”, Bitlis Eren University Journal of Science and Technology, vol. 5, no. 1, pp. 29–30, 2015, doi: 10.17678/beujst.68121.