NOWHERE-ZERO -FLOWS IN TWO FAMILIES OF VERTEX-TRANSITIVE GRAPHS

Let $\Gamma $ be a graph of valency at least four whose automorphism group contains a minimally vertex-transitive subgroup G. It is proved that $\Gamma $ admits a nowhere-zero $3$ -flow if one of the following two conditions holds: (i) $\Gamma $ is of order twice an odd number and G contains a central involution; (ii) G is a direct product of a $2$ -subgroup and a subgroup of odd order.