Nowhere-zero 3-flows in Cayley graphs on generalized dihedral group and generalized quaternion group

摘要

Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we show that this conjecture is true for Cayley graph on generalized dihedral groups and generalized quaternion groups, which generalizes the result of F. Yang and X. Li [Inform. Process. Lett., 2011, 111: 416-419]. We also generalizes an early result of M. Nanasiova and M. Skoviera [J. Algebraic Combin., 2009, 30: 103-110].