Eigenvalues of block graph

Question

Let us consider a graph $G$ having $m$ number of complete sub-graphs $K_{n_1},K_{n_2},...,K_{n_m}$ which have size $n_1,n_2,...,n_m$ respectively. Further $\forall i$, one vertex of $K_{n_i}$ is connected to one vertex of $K_{n_{i+1}}$ by an edge. Similarly, one vertex (different from previous one) of $K_{n_i}$ is connected to one vertex of $K_{n_{i-1}}$ by an edge. In this way, complete sub-graphs are connected in chain to form $G$. Find the eigenvalues of adjacency matrix of $G$.