Directed Graphs and Int-Graphic Topology

Abstract

In this work, we construct a topology $\mathcal{T}^{int}_{G}$ on the vertices set of a directed graph $G=(V,E)$.
We investigate the fact that $(V,\mathcal{T}^{int}_{G})$ is
an Alexandroff space to study some topological properties of the graph due to the existence of minimal basis for $\mathcal{T}^{int}_{G}$. Some
continuity properties of functions are proved.
Finally, some examples are given with connected and disconnected int-graphic topologies.