an:06342069
Zbl 1301.05298
Krop, Elliot; Minion, Sarah; Patel, Pritul; Raridan, Christopher
A solution to the edge-balanced index set problem for complete odd bipartite graphs
EN
Bull. Inst. Comb. Appl. 70, 119-125 (2014).
00331552
2014
j
05C78 05C25
complete bipartite graph; edge-labeling; vertex-labeling; edge-friendly labeling; edge-balanced index set
Summary: \textit{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 \(m = n\). \textit{E. Krop} and \textit{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.
Zbl 1211.05149; Zbl 1247.05209