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 <em>Γ<sup>c</sup></em> whose vertex set is 𝑃(𝑋) in which two distinct vertices 𝐴 and 𝐵 are adjacent if <em>A</em>'∩<em>B</em>' ⊆ (<em>A</em>∩<em>B</em>)'. In this paper, the closure graph is shown as a simple, connected graph with diameter at most two. Furthermore, the girth of the closure graph <em>Γ<sup>c</sup></em>of 𝑇 is three if 𝑋 contains more than one point. Also, several graph properties are studied.
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