Topologies Induced by Neighborhoods of a Graph Under Some Binary Operations

Authors

  • Anabel Enriquez Gamorez Western Mindanao State University
  • Caen Grace Nianga
  • Sergio Canoy Jr. Mindanao State Unversity- Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i3.3464

Keywords:

Topology, Graph, Edge corona, disjunction, symmetric difference

Abstract

Let G = (V (G), E(G)) be any undirected graph. Then G induces a topology τ_G on V (G) with base consisting of sets of the form F_G[A] = V (G)\N_G[A], where N_G[A] = A ∪ { x : xa ∈ E(G) for some a ∈ A } and A ranges over all subsets of V (G). In this paper, we describe the topologies induced by the corona, edge corona, disjunction, symmetric difference, Tensor product, and the strong product of two graphs by determining the subbasic open sets.

Author Biography

  • Anabel Enriquez Gamorez, Western Mindanao State University
    Mathematics and Statistics Department

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Published

2019-07-25

Issue

Vol. 12 No. 3: (July 2019)

Section

Nonlinear Analysis

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How to Cite

Topologies Induced by Neighborhoods of a Graph Under Some Binary Operations. (2019). European Journal of Pure and Applied Mathematics, 12(3), 749-755. https://doi.org/10.29020/nybg.ejpam.v12i3.3464