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arXiv · 1307.8071

A Solution to the Edge-Balanced Index Set Problem for Complete Odd Bipartite Graphs

E. Krop·S. Minion·P. Patel·C. Raridan
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Abstract

In 2009, Kong, Wang, and Lee 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. In 2011, Krop and Sikes expanded upon that work by finding EBI(K_{m,m-2a}) for odd m > 5 and 1 <= a <= (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.

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E. Krop, S. Minion, P. Patel, C. Raridan. 2013-07-30. A Solution to the Edge-Balanced Index Set Problem for Complete Odd Bipartite Graphs. https://arxiv.org/abs/1307.8071

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