Hamiltonian iterated line graphs Original Research Article

The n-iterated line graph of a graph G is Ln(G)=L(Ln−1(G)), where L1(G) denotes the line graph L(G) of G, and Ln−1(G) is assumed to be nonempty. Harary and Nash-Williams characterized those graphs G for which L(G) is hamiltonian. In this paper, we will give a characterization of those graphs G for which Ln(G) is hamiltonian, for each n⩾2. This is not a simple consequence of Harary and Nash-Williams’ result. As an application, we show two methods for determining the hamiltonian index of a graph and enhance various results on the hamiltonian index known earlier.