MAXIMAL GRAPHICAL REALIZATION OF A TOPOLOGY
DOI:
https://doi.org/10.22199/issn.0717-6279-5696Keywords:
Set-indexer; topology; t-set-graceful; optimal space.Abstract
Given a topological space, the graphical realizations of it with as many edges as possible, called maximal graphical realizations, are studied here. Every finite topological space admits a maximal graphical realization. However, there are graphs which are not maximal graphical realizations of any topology. A tree of odd order is never a maximal graphical realization of a topological space. Maximal graphical realization of a topology is a cycle if and only if it is C_3. It is shown that chain topologies admit unique maximal graphical realizations. A lower bound for the size of a maximal graphical realization is also obtained.
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