## Abstract

Let G be a 2-edge-connected undirected graph, A be an (additive) abelian group and A∗= A-{0}. A graph G is A-connected if G has an orientation D(G) such that for every function b: V(G) → A satisfying ∑v ϵ V(G)b(v) = 0, there is a function f: E(G) →A∗such that for each vertex v ϵ V(G), the total amount of f values on the edges directed out from v minus the total amount of f values on the edges directed into v equals b(v). Let Z_{3} denote the group of order 3. Jaeger et al. conjectured that there exists an integer k such that every k-edge-connected graph is Z_{3}-connected. In this paper, we prove that every N_{2}-locally connected claw-free graph G with minimum degree δ(G) ≥ 7 is Z_{3}-connected.

Original language | English (US) |
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Pages (from-to) | 193-201 |

Number of pages | 9 |

Journal | Discrete Mathematics, Algorithms and Applications |

Volume | 3 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2011 |

Externally published | Yes |

## Keywords

- Group connectivity
- claw-free graphs
- locally connectedness
- nowhere-zero flows

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

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