On Graphs of Dualities of Bipartite Posets

Year 2015, , 29 - 30, 23.06.2015

Selçuk Topal

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.

Keywords

Poset, Lower-minimal graph, Upper-maximal graph

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.