Maximal graphical realization of a topology




Set-indexer, topology, t-set-graceful, optimal space


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.

Author Biography

Ullas Thomas, St Berchmans College.

Assistant Professor in Mathematics


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How to Cite

U. Thomas and S. C. Mathew, “Maximal graphical realization of a topology”, Proyecciones (Antofagasta, On line), vol. 43, no. 2, pp. 365-382, Apr. 2024.




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