Nowhere-zero 3-flows in semistrong product of graphs

Let G and H be two graphs. The semistrong product G
- H is the graph with vertex set V(G
- H)=V(G)×V(H) and edge set E(G
- H)={(u1,v1)(u2,v2)|u1u2∈E(G)  and  v1v2∈E(H)  or  u1=u2  and  v1v2∈E(H)}. It is proved in this paper that if G and H are two nontrivial connected simple graphs, then G
- H admits a nowhere-zero 3-flow. This result extends the study of nowhere-zero flows on product graphs by Imrich and Å krekovski, by Shu and Zhang, by Rollová and Å koviera, and by others.