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A solution to the edge-balanced index set problem for complete odd bipartite graphs. (English) Zbl 1301.05298
Summary: M. C. Kong et al. [Congr. Numerantium 196, 71–94 (2009; Zbl 1211.05149)] began work on the problem of finding the edge-balanced index sets (EBI) of complete bipartite graphs $$K_{m,n}$$ by solving the cases where $$n = 1, 2, 3, 4$$, and 5, and also the case where $$m = n$$. E. Krop and K. Sikes [ibid. 207, 23–32 (2011; Zbl 1247.05209)] expanded upon that work by finding $$\mathrm{EBI}(K_{m,m-2a})$$ for odd $$m > 5$$ and $$1\leq a \leq \frac{m-3}{4}$$. In this paper, we provide a general solution to the edge-balanced index set problem for all complete odd bipartite graphs, thereby concluding the problem for this case.
##### MSC:
 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 05C25 Graphs and abstract algebra (groups, rings, fields, etc.)