Abstract The affine Deligne–Lusztig variety $X_w(b)$ in the flag of a reductive group ${\mathbf G}$ depends on two parameters: $\sigma $ -conjugacy class $[b]$ and element w Iwahori–Weyl $\tilde {W}$ . In this paper, for any given , we determine nonemptiness pattern dimension formula most $w \in \tilde

In this paper, we used the permutation group together with concept of cordiality in graph theory to introduce a new method labeling. This construed permuted cordial labeling can be applied all paths, cycles, fans and wheel graphs. Moreover, some other properties are investigated show that union any two paths cycles addition, for path cycle.