On graphs associated to topological spaces - Haval Mohammed Salih (Indonesian Combinatorial Society (InaCombS), 2023)
Let ???? be a set and (????,????) be a topological space. A new type of graph on ????(????), namely the closure graph of ???? is introduced. The closure graph denoted by Γc whose vertex set is ????(????) in which two distinct vertices ???? and ???? are adjacent if A'∩B' ⊆ (A∩B)'. 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 Γcof ???? is three if ???? contains more than one point. Also, several graph properties are studied.