Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651261 | Discrete Mathematics | 2006 | 5 Pages |
Abstract
Let ΓΓ be an abelian group. Jaeger et al. [Group connectivity of graphs—a nonhomogeneous analogue of nowhere-zero flow properties, J. Combin. Theory Ser. B 56 (1992) 165–182] introduced a class of graphs which they call ΓΓ-connected. The main interest in ΓΓ-connected graphs is that every ΓΓ-connected graph admits a nowhere-zero ΓΓ-flow. In this paper, we found some families of Z3Z3-connected graphs. Our results generalize an early theorem by Lai (Nowhere-zero 3-flows in locally connected graphs, J. Graph Theory 42 (2003) 211–219) for nowhere-zero Z3Z3-flows in locally connected graphs, and provide a simplified proof of a theorem of Xu and Zhang on nowhere-zero Z3Z3-flows in squares of graphs.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Matt DeVos, Rui Xu, Gexin Yu,