In this paper, new graphs $G_τ=\left(V,E\right)$ are constructed from the discrete topological space $(X,τ)\ $ . Several properties of this type of graphs are given such that: the clique number equals the number of elements in X also the number of pendants vertices, $G_τ$ has no isolated vertices, the minimum degree in $G_τ$ is one and maximum degree equal $n-1+\sum^{n-1}_{i=2}\binom{n-1}{i}$ , the minimum dominating set is determined and $γ(G_τ)$ is evaluated for $G_τ$ and for corona and join operations between to discrete topological graphs. At what matter $β\left(G_τ\right)=γ(G_τ)$ is discussed for $G_τ$. Also that $G_τ$ is proved a connected graph of order $2^n-2$ and it has no isolated vertex. Then, rad $\ G_τ$ and diam $\ (G_τ)$ are evaluated.