The most general structure of graphs with hamiltonian or hamiltonian connected square

On the basis of recent results on hamiltonicity, [5], and hamiltonian connectedness, [9], in the square of a 2-block, we determine the most general block-cutvertex structure a graph G may have in order to guarantee that G2 is hamiltonian, hamiltonian connected, respectively. Such an approach was already developed in [10] for hamiltonian total graphs.