On Topologies Induced by Graphs Under Some Unary and Binary Operations
DOI:
https://doi.org/10.29020/nybg.ejpam.v12i2.3421Abstract
Let G = (V (G),E(G)) be any simple undirected graph. The open hop neighborhood of v ϵ V(G) is the set ð‘_ðº^2(ð‘£) = {u ϵ V(G): ð‘‘_ðº (u,v) = 2}. Then G induces a topology τ_G on V (G) with base consisting of sets of the form F_G^2[A] = V(G) \ N_G^2 [A] where N_G^2 [A] = A ∪ {v ϵ V(G):  ð‘_ðº^2(ð‘£) ∩ A ≠∅ } 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.Downloads
Published
2019-04-29
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Algebra
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How to Cite
On Topologies Induced by Graphs Under Some Unary and Binary Operations. (2019). European Journal of Pure and Applied Mathematics, 12(2), 499-505. https://doi.org/10.29020/nybg.ejpam.v12i2.3421