### Abstract

A k-container of G between u and v, C(u,v), is a set of k internally disjoint paths between u and v. A k^{*}-container C(u,v) of G is a k-container if it contains all vertices of G. A graph G is k ^{*}-connected if there exists a k^{*}-container between any two distinct vertices. Thus, every 1^{*}-connected graph is Hamiltonian connected. Moreover, every 2^{*}-connected graph is Hamiltonian. Zhan proved that G=L(M) is Hamiltonian connected if the edge-connectivity of M is at least 4. In this paper, we generalize this result by proving G=L(M) is k^{*}-connected if the edge-connectivity of M is at least max2k,4. We also generalize our result into spanning fan-connectivity.

Original language | English |
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Pages (from-to) | 1614-1617 |

Number of pages | 4 |

Journal | Applied Mathematics Letters |

Volume | 24 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2011 Sep 1 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

*Applied Mathematics Letters*,

*24*(9), 1614-1617. https://doi.org/10.1016/j.aml.2011.04.013

}

*Applied Mathematics Letters*, vol. 24, no. 9, pp. 1614-1617. https://doi.org/10.1016/j.aml.2011.04.013

**The spanning connectivity of line graphs.** / Huang, Po-Yi; Hsu, Lih Hsing.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The spanning connectivity of line graphs

AU - Huang, Po-Yi

AU - Hsu, Lih Hsing

PY - 2011/9/1

Y1 - 2011/9/1

N2 - A k-container of G between u and v, C(u,v), is a set of k internally disjoint paths between u and v. A k*-container C(u,v) of G is a k-container if it contains all vertices of G. A graph G is k *-connected if there exists a k*-container between any two distinct vertices. Thus, every 1*-connected graph is Hamiltonian connected. Moreover, every 2*-connected graph is Hamiltonian. Zhan proved that G=L(M) is Hamiltonian connected if the edge-connectivity of M is at least 4. In this paper, we generalize this result by proving G=L(M) is k*-connected if the edge-connectivity of M is at least max2k,4. We also generalize our result into spanning fan-connectivity.

AB - A k-container of G between u and v, C(u,v), is a set of k internally disjoint paths between u and v. A k*-container C(u,v) of G is a k-container if it contains all vertices of G. A graph G is k *-connected if there exists a k*-container between any two distinct vertices. Thus, every 1*-connected graph is Hamiltonian connected. Moreover, every 2*-connected graph is Hamiltonian. Zhan proved that G=L(M) is Hamiltonian connected if the edge-connectivity of M is at least 4. In this paper, we generalize this result by proving G=L(M) is k*-connected if the edge-connectivity of M is at least max2k,4. We also generalize our result into spanning fan-connectivity.

UR - http://www.scopus.com/inward/record.url?scp=79956140335&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79956140335&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2011.04.013

DO - 10.1016/j.aml.2011.04.013

M3 - Article

AN - SCOPUS:79956140335

VL - 24

SP - 1614

EP - 1617

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

IS - 9

ER -