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Enumerations of Finite Topologies Associated with a Finite Simple Graph
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  • Journal title : Kyungpook mathematical journal
  • Volume 54, Issue 4,  2014, pp.655-665
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2014.54.4.655
 Title & Authors
Enumerations of Finite Topologies Associated with a Finite Simple Graph
Kim, Dongseok; Kwon, Young Soo; Lee, Jaeun;
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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.
finite topology;preorder;graph;
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