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On the edge-balanced index sets of complete bipartite graphs. (English) Zbl 1247.05209
Summary: Let \(G\) be a graph with vertex set \(V(G)\) and edge set \(E(G)\), and \(f\) be a \(0-1\) labeling of \(E(G)\) so that the absolute difference in the number of edges labeled \(1\) and \(0\) is no more than one. Call such a labeling \(f\) edge-friendly. The edge-balanced index set of the graph \(G\), \(\text{EBI}(G)\), is defined as the absolute difference between the number of vertices incident to more edges labeled \(1\) and the number of vertices incident to more edges labeled \(0\) over all edge-friendly labelings \(f\).
In [Congr. Numerantium 196, 71–94 (2009; Zbl 1211.05149)], S.-M. Lee, M. Kong and Y.-C. Wang found the \(\text{EBI}(K_{l,n})\) for \(l=1, 2,3,4,5\) as well as \(l=n\). We continue the investigation of the EBI of complete bipartite graphs of other orders.

MSC:
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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