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A152946 Magic deficiency of the complete graph K_n on n vertices. 0
0, 0, 0, 1, 0, 0, 4, 10, 19, 31, 44 (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)=1 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 of K_4 using the set {1,2,...,11}\{4}, with largest label 11.

Hence the magic deficiency of K_4 is a(4)=11-10=1.


See sequence A152682. The n-th term of the magic deficiency sequence equals the n-th term of sequence A152682 minus "n+{n choose 2}".

(The number "n+{n choose 2}" is the total number of vertices and edges in K_n.)

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

Sequence in context: A008038 A301248 A160425 * A162505 A025720 A022793

Adjacent sequences:  A152943 A152944 A152945 * A152947 A152948 A152949




John P. McSorley, Dec 15 2008



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