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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...
Let G be a 2-edge-connected simple graph on n vertices, let A denote an abelian group with the identity element 0, and let D be an orientation of G. The boundary of a function f:E(G)→A is the function ∂f:V(G)→A given by ∂f(v)=∑e∈E+(v)f(e)−∑e∈E−(v)f(e), where E+(v) is the set of edges with tail v and E−(v) is the set of edges with head v. A graph G is A-connected if for every b:V(G)→A with ∑v∈V(G)b(v)=0,...
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