GRAPHIC TOPOLOGY ON FUZZY GRAPHS

Abstract

In this paper, we study the graphic topology $\mathcal{T}_{G}$ for a fuzzy graph. We give some properties of this topology, in particular we prove that $\mathcal{T}_{G}$ is an Alexandroff topology and when two graphs are isomorphic, their graphic topologies will be homeomorphic. We give some properties matching graphs and homeomorphic topology spaces. Finally, we investigate the connectedness of this topology and some relations between the connectedness of the graph and the topology $\mathcal{T}_{G}$.