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On the edge-balanced index sets of complete even bipartite graphs. (English) Zbl 1334.05139
Summary: In [Congr. Numerantium 196, 71–94 (2009; Zbl 1211.05149)], M. C. Kong et al. introduced the problem of finding the edge-balanced index sets (EBI) of complete bipartite graphs $$K_{m,n}$$ by examining the cases where $$m\geq n$$ and $$n=1,2,3,4$$, and $$5$$, as well as the case where $$m=n\geq 6$$. Since then, the problem of finding $$\operatorname{EBI}(K_{m,n})$$ has been solved in the case where $$m\geq n\geq 1$$ are both odd and in the case where $$m$$ is odd, $$n$$ is even, and $$m>n$$. In this paper, we find the edge-balanced index sets for complete even bipartite graphs. That is, we solve the $$\operatorname{EBI}(K_{m,n})$$ problem in the case where $$m\geq n\geq 2$$ are both even.
##### MSC:
 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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