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Xiong and Liu [L. Xiong and Z. Liu, Hamiltonian iterated line graphs,Discrete Math. 256 (2002) 407-422] gave a characterization of the graphs $G$for which the $n$-th iterated line graph $L^n(G)$ is hamiltonian, for $n\ge2$.In this paper, we study the existence of a hamiltonian path in $L^n(G)$, andgive a characterization of $G$ for which $L^n(G)$ has a hamiltonian path. Asapplications, we use this characterization to give several upper bounds on thehamiltonian path index of a graph.

On traceable iterated line graph and hamiltonian path index