Geodesic
Enumerating families of labeled graphs
Journal of integer sequences, Tome 18 (2015) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In 1966, Rosa introduced, among others, $\alpha $- and $\beta $-labelings as tools to solve the isomorphic decomposition problem of the complete graph. Ten years later, Sheppard calculated the number of $\alpha $- and $\beta $-labeled graphs with $n$ edges. In this paper we use an extended version of the adjacency matrix of a graph to determine the number of gracefully labeled graphs with $n$ edges; furthermore, we also calculate the number of them with $m$ vertices for every suitable value of $m$. In addition, we use this technique to determine the number of labeled graphs for other types of labelings as the harmonious, felicitous, and elegant.
Classification : 05C30, 05C78
Keywords: graceful graph, $\alpha $-graph, enumeration, graceful triangle 
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     author = {Barrientos, Christian and Minion, Sarah},
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Barrientos, Christian; Minion, Sarah. Enumerating families of labeled graphs. Journal of integer sequences, Tome 18 (2015) no. 1. http://geodesic.mathdoc.fr/item/JIS_2015__18_1_a7/