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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 (list; graph; refs; listen; history; text; internal format)



W. D. Wallis. Magic Graphs. Birkhauser, (2001). Section 2.10.


Table of n, a(n) for n=1..11.

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.


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.


See related sequence A129413 which concerns the smallest value of the magic sum of an edge-magic injection of K_n.

Sequence in context: A287075 A263260 A324773 * A059753 A256001 A131665

Adjacent sequences:  A152679 A152680 A152681 * A152683 A152684 A152685




John P. McSorley, Dec 10 2008



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