Intersection Orbital Graphs of Permutation Groups and Reconstruction of Simple Groups

We introduce the \emph{intersection orbital graph} $\mathrm{\Gamma }(G_1,G_2;\mathrm{\Omega })$ associated with two permutation groups $G_1,G_2\le \mathrm{S}\mathrm{y}\mathrm{m}(\mathrm{\Omega })$ on a finite set $\mathrm{\Omega }$.