The validity of Tutte's 3-flow conjecture for some Cayley graphs
Keywords:Nowhere-zero flow, Cayley graph, Tutte's 3-flow conjecture, connection sequence, solvable group, nilpotent group
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.