Abstract
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.
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