2011/06/06 by Elliot Krop, Krop, Elliot, Keli Sikes +1
Computer Science · Engineering · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1106.1085
openalex publication_date 2011/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citeLeeKongWang 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.