On graphs associated to topological spaces

Haval Mohammed Salih

Abstract


Let 𝑋 be a set and (𝑋,𝑇) be a topological space. A new type of graph on 𝑃(𝑋), namely the closure graph of 𝑇 is introduced. The closure graph denoted by Ξ“cΒ whose vertex set is 𝑃(𝑋) in which two distinct vertices 𝐴 and 𝐡 are adjacent if A'∩B'Β βŠ† (A∩B)'.Β In this paper, the closure graph is shown as a simple, connected graph with diameter at most two. Furthermore, the girth of the closure graphΒ Ξ“cof 𝑇 is three if 𝑋 contains more than one point. Also, several graph properties are studied.

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DOI: http://dx.doi.org/10.19184/ijc.2023.7.1.5

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