The validity of Tutte's 3-flow conjecture for some Cayley graphs - Ahanjideh, Milad (Ars mathematica contemporanea, 2019)
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.
Keywords: Cayley graph; Cayleyjev graf; connection sequence; nilpotent group; nilpotentna grupa; nowhere-zero flow; povsod neničelni tok; rešljiva grupa; solvable group; Tutte's 3-flow conjecture; Tuttova domneva o 3-toku; zaporedje povezav