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A308722
Number of edges in the smallest possible regular graceful graph of valence n.
0
0, 1, 3, 6, 12, 20, 27, 35, 48, 63, 75, 99, 108
OFFSET
0,3
COMMENTS
A graceful graph with e edges is one that allows a labeling of its vertices with distinct integers between 0 and e, inclusive, such that when each edge is labeled with the absolute difference of the labels of its endpoints, these edge labels will be exactly the integers between 1 and e, inclusive.
This sequence counts the minimal number edges possible, in a regular graceful graph of valence n.
The concept was introduced by Ed Pegg in a post on Mathematics Stack Exchange; all the data here is from that post.
Pegg conjectures that the sequence continues (from n = 13): 130, 147, 180, 192, 221, 243, 285, 320, 336.
EXAMPLE
See the link at Mathematics Stack Exchange.
CROSSREFS
Sequence in context: A181962 A226220 A218076 * A320192 A160732 A320608
KEYWORD
nonn,more
AUTHOR
Allan C. Wechsler, Jun 19 2019
EXTENSIONS
More terms from Ed Pegg Jr, Jul 17 2019
STATUS
approved