Maximal graphical realization of a topology

• Thomas, Ullas ^[1] ; C Mathew, Sunil ^[2]
  1. [1] S. B. College Changanassery
  2. [2] Deva Matha College Kuravilangad
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 43, Nº. 2, 2024, págs. 365-382
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.