A solution to the edge-balanced index set problem for complete odd bipartite graphs. (English) Zbl 1301.05298

Krop, Elliot; Minion, Sarah; Patel, Pritul; Raridan, Christopher

Bull. Inst. Comb. Appl. 70, 119-125 (2014).

Summary: M. C. Kong et al. [Congr. Numerantium 196, 71–94 (2009; Zbl 1211.05149)] began work on the problem of finding the edge-balanced index sets (EBI) of complete bipartite graphs \(K_{m,n}\) by solving the cases where \(n = 1, 2, 3, 4\), and 5, and also the case where \(m = n\). E. Krop and K. Sikes [ibid. 207, 23–32 (2011; Zbl 1247.05209)] expanded upon that work by finding \(\mathrm{EBI}(K_{m,m-2a})\) for odd \(m > 5\) and \(1\leq a \leq \frac{m-3}{4}\). In this paper, we provide a general solution to the edge-balanced index set problem for all complete odd bipartite graphs, thereby concluding the problem for this case.

MSC:

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

Keywords:

complete bipartite graph; edge-labeling; vertex-labeling; edge-friendly labeling; edge-balanced index set