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On the enumeration of finite maximal connected topologies
1973
Journal of combinatorial theory. Series B (Print)
A connected topology F is said to be maximal connected if ?# strictly finer than Y implies that % is disconnected. In this paper, it is shown that the number of homeomorphism classes of maximal connected topologies defined on a set with n points is equal to twice the number of n point trees minus the number of n point trees possessing a symmetry line. An enumeration of a class of topologies, called critical connected topologies, which includes the maximal connected spaces is then carried out
doi:10.1016/0095-8956(73)90020-8
fatcat:vnp6ibdcxnecjap4oms2bsdz5m