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A152946 Magic deficiency of the complete graph K_n on n vertices. 0


%S 0,0,0,1,0,0,4,10,19,31,44

%N Magic deficiency of the complete graph K_n on n vertices.

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

%H A. Kotzig and A. Rosa, <a href="http://dx.doi.org/10.4153/CMB-1970-084-1">Magic Valuations of Finite Graphs</a>, Canad. Math. Bull. v.13 (1970), pp. 451-461.

%H J. P. McSorley and J. A. Trono, <a href="https://doi.org/10.1016/j.disc.2009.07.021">On k-minimum and m-minimum Edge-Magic Injections of Graphs</a>, Discrete Mathematics, Volume 310, Issue 1, 6 January 2010, Pages 56-69.

%e 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.

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

%Y 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}".

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

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

%K nonn,more

%O 1,7

%A _John P. McSorley_, Dec 15 2008

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