Theorem :- A lattice L is not a distributive lattice if and only if L has a sublattice which is isomorphic Kite structure Lattice^{ }or pantagon Structure Lattice
Kite lattice and Pantagon lattice:
These two are not satisfying distributive property i.e. $x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z)$
So Graph contain these two also not distributive.