Z-graphic topology on undirected graph

Kuwait Journal of Science

article

Hanan Omer Zomam¹  Makkia Dammak² 

[1] Dept. of Mathematics, College of Science, Taibah University;Dept. of Mathematics, Faculty of Sciences, University of Sfax

关键词: Connected components;    homeomorphism;    graph;    symmetric topologies;    topology;   

DOI  :  10.48129/kjs.17541

学科分类：社会科学、人文和艺术（综合）

来源: Kuwait University * Academic Publication Council

【 摘 要 】

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.

【 授权许可】

Unknown