Flow-contractible configurations and group connectivity of signed graphs

Jaeger, Linial, Payan and Tarsi (JCTB, 1992) introduced the concept of group connectivity as a generalization of nowhere-zero flow for graphs. In this paper, we introduce group connectivity for signed graphs and establish some fundamental properties. For a finite abelian group A, it is proved that an A-connected signed graph is a contractible configuration for A-flow problem of signed graphs. In addition, we give sufficient edge connectivity conditions for signed graphs to be A-connected and study the group connectivity of some families of signed graphs.