Abstract
Let G and H be two graphs. The semistrong productG•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 Škrekovski, by Shu and Zhang, by Rollová and Škoviera, and by others.
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