Walks, Paths and Connectivity · Hard problem

Let $G$ consist of two copies of $K_4$ that share exactly one vertex: one $K_4$ on vertices $1,2,3,4$ and the other on vertices $1,5,6,7$ (so vertex $1$ belongs to both, and there is no edge directly joining $\{2,3,4\}$ to $\{5,6,7\}$). Find $\lambda(G) - \kappa(G)$.