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 rst 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 a ects the value of the hamiltonian index of a graph G