Hamiltonian iterated line graphs

Authors:
Liming Xiong;Zhanhong Liu
Affiliations:
Department of Mathematics, Jiangxi Normal University, Nanchang 330027, People's Republic of China;Department of Mathematics, Jiangxi Normal University, Nanchang 330027, People's Republic of China
Venue:
Discrete Mathematics
Year:
2002

Citing 8
Cited 3

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A simple upper bound for the Hamiltonian index of a graph

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Note: Hamiltonian index is NP-complete

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Abstract

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.