Geodesic
On the Number of α-Labeled Graphs
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 177-188.

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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.
Keywords: α -labeling, α -graph, graceful triangle 
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Barrientos, Christian; Minion, Sarah. On the Number of α-Labeled Graphs. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 177-188. http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a14/

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