On the number of α-labeled graphs
Christan Barrientos, Sarah Minion · Discussiones Mathematicae Graph Theory · 2017
When a graceful labeling of a bipartite graph places the smaller labels in one of the stable sets of the graph, it becomes an -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 -labeled graphs according to their size, order, and boundary value.