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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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