Hamiltonian iterated line graphs

Liming Xiong; Zhanhong Liu

doi:10.1016/S0012-365X(01)00442-3

Hamiltonian iterated line graphs

Liming Xiong^*, Zhanhong Liu

^*Corresponding author for this work

Jiangxi Normal University

Research output: Contribution to journal › Article › peer-review

31 Citations (Scopus)

Abstract

The n-iterated line graph of a graph G is Lⁿ(G) = L(L^n-1G)), where L¹G) 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 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.

Original language	English
Pages (from-to)	407-422
Number of pages	16
Journal	Discrete Mathematics
Volume	256
Issue number	1-2
DOIs	https://doi.org/10.1016/S0012-365X(01)00442-3
Publication status	Published - 28 Sept 2002
Externally published	Yes

Keywords

Complexity
Contraction of graphs
Hamiltonian index
Iterated line graph
Split block

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10.1016/S0012-365X(01)00442-3

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title = "Hamiltonian iterated line graphs",

abstract = "The n-iterated line graph of a graph G is Ln(G) = L(Ln-1G)), where L1G) 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.",

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T1 - Hamiltonian iterated line graphs

AU - Xiong, Liming

AU - Liu, Zhanhong

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N2 - The n-iterated line graph of a graph G is Ln(G) = L(Ln-1G)), where L1G) 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.

AB - The n-iterated line graph of a graph G is Ln(G) = L(Ln-1G)), where L1G) 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.

KW - Complexity

KW - Contraction of graphs

KW - Hamiltonian index

KW - Iterated line graph

KW - Split block

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VL - 256

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EP - 422

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-2

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Hamiltonian iterated line graphs

Abstract

Keywords

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