On Stability of the Hamiltonian Index under Contractions and Closures

The hamiltonian index of a graph G is the smallest integer k such that the k-th iterated line graph of G is hamiltonian. We first show that, with one exceptional case, adding an edge to a graph cannot increase its hamiltonian index. We use this result to prove that neither the contraction of an AG (F)-contractible subgraph F of a graph G nor the closure operation performed on G (if G is claw-free) affects the value of the hamiltonian index of a graph G