Topologies Induced by Neighborhoods of a Graph Under Some Binary Operations

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.