Z-graphic topology on undirected graph

10.48129/kjs.17541

Abstract

In this work, we define $\mathcal{Z}_{G}$ a topology on the vertex set of a graph $G$ which preserves the connectivity of the graph, called $\mathcal{Z}$-graphic topology. We prove that two isomorphic graphs have homeomorphic and symmetric $\mathcal{Z}$-graphic topologies. We show that $\mathcal{Z}_{G}$ is an Alexandroff topology and we give a necessary and sufficient condition for a topology to be $\mathcal{Z}$-graphic.