@article{On Topologies Induced by Graphs Under Some Unary and Binary Operations_2019, place={Maryland, USA}, volume={12}, url={https://www.ejpam.com/index.php/ejpam/article/view/3421}, DOI={10.29020/nybg.ejpam.v12i2.3421}, abstractNote={Let G = (V (G),E(G)) be any simple undirected graph. The open hop neighborhood ofÂ v Ïµ V(G)Â is the set ð‘_ðº^2(ð‘£) = {u Ïµ V(G):Â ð‘‘_ðº (u,v) = 2}.Â Then G induces a topologyÂ Ï„_G on V (G) with base consisting of sets of the formÂ F_G^2[A] = V(G) \ N_G^2 [A] whereÂ N_G^2 [A] = A âˆª {vÂ Ïµ V(G):Â Â ð‘_ðº^2(ð‘£)Â âˆ© A â‰ âˆ… } and A ranges over all subsets of V (G). In this paper, we describe the topologies induced by the complement of a graph, the join, the corona, the composition and the Cartesian product of graphs.}, number={2}, journal={European Journal of Pure and Applied Mathematics}, year={2019}, month={Apr.}, pages={499–505} }