On Topologies Induced by Graphs Under Some Unary and Binary Operations

Authors

  • Caen Grace Sarona Nianga
  • Sergio R. Canoy Jr.

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i2.3421

Abstract

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.

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How to Cite

Nianga, C. G. S., & Canoy Jr., S. R. (2019). On Topologies Induced by Graphs Under Some Unary and Binary Operations. European Journal of Pure and Applied Mathematics, 12(2), 499–505. https://doi.org/10.29020/nybg.ejpam.v12i2.3421