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Enumerations of finite topologies associated with a finite graph

Combinatorics 2014-12-30 v1 General Topology

Abstract

The number of topologies and non-homeomorphic topologies on a fixed finite set are now known up to n=18n=18, n=16n=16 but still no complete formula yet (Sloane). There are one to one correspondence among topologies, preorder and digraphs. In this article, we enumerate topologies and non-homeomorphic topologies whose underlying graph is a given finite graph.

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Cite

@article{arxiv.1206.0550,
  title  = {Enumerations of finite topologies associated with a finite graph},
  author = {Dongseok Kim and Young Soo Kwon and Jaeun Lee},
  journal= {arXiv preprint arXiv:1206.0550},
  year   = {2014}
}

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