Enumerating Families of Labeled Graphs
Christian Barrientos and Sarah Minion
Department of Mathematics
Clayton State University
Morrow, GA 30260
In 1966, Rosa introduced, among others, α- and β-labelings
as tools to solve the isomorphic decomposition problem of the complete
graph. Ten years later, Sheppard calculated the number of α- and
β-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.
Full version: pdf,
(Concerned with sequences
July 22 2014;
revised versions received November 16 2014; December 5 2014.
Published in Journal of Integer Sequences, January 12 2015.
Journal of Integer Sequences home page