login
A152682
The smallest value of the largest label for which there exists an edge-magic injection of the complete graph K_n on n vertices.
1
1, 3, 6, 11, 15, 21, 32, 46, 64, 86, 110
OFFSET
1,2
REFERENCES
W. D. Wallis. Magic Graphs. Birkhäuser, (2001). Section 2.10.
LINKS
A. Kotzig and A. Rosa, Magic Valuations of Finite Graphs, Canad. Math. Bull. v.13 (1970), pp. 451-461.
J. P. McSorley and J. A. Trono, On k-minimum and m-minimum Edge-Magic Injections of Graphs, Discrete Mathematics, Volume 310, Issue 1, 6 January 2010, Pages 56-69.
EXAMPLE
a(4)=11 because when forming an edge-magic injection of K_4 we must use at least the first 10 natural numbers {1,2,...10} since K_4 has a total of 10 vertices and edges. However this is not possible. But there is an edge-magic injection using the set {1,2,....11}\{4}, namely with {1,2,3,5} as the vertex labels.
CROSSREFS
See related sequence A129413 which concerns the smallest value of the magic sum of an edge-magic injection of K_n.
Sequence in context: A263260 A324773 A373189 * A059753 A256001 A131665
KEYWORD
nonn,more
AUTHOR
John P. McSorley, Dec 10 2008
STATUS
approved