### 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 G such that for every map b : V(G) → A satisfying v V(G) b(v) = 0, there is a function f : E(G) → Asuch that for each vertex v 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). Jaeger et al. [F. Jaeger, N. Linial, C. Payan, M. Tarsi, Group connectivity of graphs-a nonhomogeneous analogue of nowhere-zero flow properties, J. Combinatorial Theory, Series B 56 (1992) 165-182] conjectured that every 5-edge-connected graph G is Z _{3}-connected, where Z3 is the cyclic group of order 3. In this paper we prove that every connected Cayley graph G of degree at least 5 on an Abelian group is Z_{3}-connected.

Original language | English (US) |
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Pages (from-to) | 1666-1676 |

Number of pages | 11 |

Journal | Discrete Mathematics |

Volume | 313 |

Issue number | 16 |

DOIs | |

Publication status | Published - Jan 1 2013 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Cite this

_{3}-connectivity in Abelian Cayley graphs.

*Discrete Mathematics*,

*313*(16), 1666-1676. https://doi.org/10.1016/j.disc.2013.04.008