Authors: Yihao Guo, Xiangjuan Yao
LetG be an undirected graph, A be an (additive) abelian group and * A = A- {0}.A graph G is A -connected if G has an orientation D(G) such that for every function b :V(G) ® A satisfyinvÎ V(G),b(v) =0, there is a function * f : E(G) ® A such that at each vertex v Î V(G), ( ) ( ) e ED v f e + Î å - ( ) ( ) e ED v f e - Î å =b(v) . In this study, we proved that if G has an odd cycle C and for every vertex ( ), ( ) 3 C vÎ V G d v = ,then G has no 3 Z - NZF . Furthermore, we proposed a few applications of this result.
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