Topologies Induced by Neighborhoods of a Graph Under Some Binary Operations

Anabel Enriquez Gamorez, Caen Grace Nianga, Sergio Canoy Jr.

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.

Keywords

Topology; Graph;Edge corona; disjunction; symmetric difference

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