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 , 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.
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}
}
Comments
2 figures