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.
@article{bwmeta1.element.doi-10_7151_dmgt_1985,
author = {Christian Barrientos and Sarah Minion},
title = {On the Number of$\alpha$-Labeled Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {38},
year = {2018},
pages = {177-188},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1985}
}
Christian Barrientos; Sarah Minion. On the Number ofα-Labeled Graphs. Discussiones Mathematicae Graph Theory, Tome 38 (2018) pp. 177-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1985/