On the Edge-balanced Index Sets of Complete Bipartite Graphs

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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, 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 2009, Lee, Kong, and Wang LeeKongWang found the EBI(Kₗ,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.