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http://dx.doi.org/10.5666/KMJ.2014.54.4.655

Enumerations of Finite Topologies Associated with a Finite Simple Graph  

Kim, Dongseok (Department of Mathematics, Kyonggi University)
Kwon, Young Soo (Department of Mathematics, Yeungnam University)
Lee, Jaeun (Department of Mathematics, Yeungnam University)
Publication Information
Kyungpook Mathematical Journal / v.54, no.4, 2014 , pp. 655-665 More about this Journal
Abstract
The number of topologies (non-homeomorphic topologies) on a fixed finite set having n elements are now known up to n = 18 (n = 16 respectively) but still no complete formula yet. There are one to one correspondences among topologies, preorders and transitive digraphs on a given finite set. In this article, we enumerate topologies and non-homeomorphic topologies whose underlying graph is a given finite simple graph.
Keywords
finite topology; preorder; graph;
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