Enumerations of Finite Topologies Associated with a Finite Simple Graph
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The number of topologies (non-homeomorphic topologies) on a fixed finiteset having n elements are now known up to n = 18 (n = 16 respectively) but still nocomplete formula yet. There are one to one correspondences among topologies, preordersand transitive digraphs on a given nite set. In this article, we enumerate topologies andnon-homeomorphic topologies whose underlying graph is a given finite simple graph.
Abstract
The number of topologies (non-homeomorphic topologies) on a fixed finiteset having n elements are now known up to n = 18 (n = 16 respectively) but still nocomplete formula yet. There are one to one correspondences among topologies, preordersand transitive digraphs on a given nite set. In this article, we enumerate topologies andnon-homeomorphic topologies whose underlying graph is a given finite simple graph.
참고문헌 (13)
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