TY - JOUR

T1 - The spanning connectivity of line graphs

AU - Huang, Po Yi

AU - Hsu, Lih Hsing

N1 - Funding Information:
This work was supported in part by the National Science Council of the Republic of China under Contract 97-2221-E-126-001-MY3 .
Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/9

Y1 - 2011/9

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.

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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 -