A Solution to the Edge-Balanced Index Set Problem for Complete Odd Bipartite Graphs
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Publication:3189192
zbMATH Open1301.05298arXiv1307.8071MaRDI QIDQ3189192
Christopher Raridan, Sarah Minion, Pritul Patel, Elliot Krop
Publication date: 9 September 2014
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.
Full work available at URL: https://arxiv.org/abs/1307.8071
Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graph labelling (graceful graphs, bandwidth, etc.) (05C78)
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