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

Abstract

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