A129413 The smallest value of a magic sum among all edge-magic injections of the complete graph K_n on n vertices.

1, 6, 9, 14, 18, 25, 38, 51, 71, 89, 116

Offset

1,2

References

W. D. Wallis. Magic Graphs. Birkhäuser, (2001). Section 2.3.3.

Links

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

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.

W. D. Wallis, E. T. Baskoro, M. Miller and Slamin, Edge-Magic Total Labellings, Australas. J. Comb. v.22, (2000), pp.177-190. Section 7.1.

Example

a(3)=9 because in an edge-magic injection of the complete graph K_3 the smallest value that the largest label used can be is 6.
Then the other two labels sum to at least 1+2.
Hence the smallest that the magic sum can be is 6+1+2=9, and such an edge-magic injection of K_3 with magic sum 9 exists.

Crossrefs

Sequence in context: A315984 A133796 A315985 * A315986 A190461 A095098

Adjacent sequences: A129410 A129411 A129412 * A129414 A129415 A129416

Keyword

nonn,more

Author

John P. McSorley, Aug 25 2008

Status

approved