Abstract

Let Γ 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 Γ-connected. The main interest in Γ-connected graphs is that every Γ-connected graph admits a nowhere-zero Γ-flow. In this paper, we found some families of Z₃-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 Z₃-flows in locally connected graphs, and provide a simplified proof of a theorem of Xu and Zhang on nowhere-zero Z₃-flows in squares of graphs.

Keywords: Integer flow; Group connectivity; Squares of graphs

Article Outline

1. Introduction

2. Proofs

Further Reading

References