1,7

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. Preprint, (2008).

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

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 defiency 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: A057312 A008038 A160425 this_sequence A025720 A022793 A005448

Adjacent sequences: A152943 A152944 A152945 this_sequence A152947 A152948 A152949

nonn

John P.McSorley (mcsorley60(AT)hotmail.com), Dec 15 2008