C. Barrientos, S. Minion
On the number of α-labeled graphs
Discussiones Mathematicae Graph Theory
Received 13.04.2015, Revised 28.10.2016, Accepted 28.10.2016, doi: 10.7151/dmgt.1985
When a graceful labeling of a bipartite graph places the smaller labels in one of the stable sets of the graph, it becomes an α-labeling. This is the most restrictive type of difference-vertex labeling and it is located at the very core of this research area. Here we use an extension of the adjacency matrix to count and classify α-labeled graphs according to their size, order, and boundary value.
α-labeling, α-graph, graceful triangle