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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
