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Tutte’s  3 -flow conjecture claims that every bridgeless graph with no  3 -edge-cut admits a nowhere-zero  3 -flow. In this paper we verify the validity of Tutte’s  3 -flow conjecture on Cayley graphs of certain classes of finite groups. In particular, we show that every Cayley graph of valency at least  4  on a generalized dicyclic group has a nowhere-zero  3 -flow. We also show that if   G   is a solvable group with a cyclic Sylow  2 -subgroup and the connection sequence   S   with  | S | ≥ 4  contains a central generator element, then the corresponding Cayley graph  Cay( G ,  S )  admits a nowhere-zero  3 -flow.

The validity of Tutte's 3-flow conjecture for some Cayley graphs