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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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