We can construct toric manifolds from simple graphs. The automorphism group of a simple graph induces a representation on the cohomology ring of the toric manifold associated to the simple graph. The automorphism group of a complete graph is a symmetric group. Procesi described the cohomology representation when the simple graph is a complete graph. In this talk we take a graph obtained by removing an edge from a complete graph and describe the associated cohomology representation.