Abstract
The n-iterated line graph of a graph G is L n ( G)= L( L n−1 ( G)), where L 1( G) denotes the line graph L( G) of G, and L n−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 L n ( 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.
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