A212661 a(n) = smallest number of edges that must be removed from K_n to obtain a graceful graph.

0, 0, 1, 2, 4, 5, 7, 9, 12, 16, 20, 23, 26, 30, 35, 41, 48, 52, 57, 63, 70, 78, 87, 93

Offset: 3

Author

N. J. A. Sloane, Jun 05 2012

Keywords

• nonn
• more

References

• G. S. Bloom and S. W. Golomb, Numbered complete graphs, unusual rulers, and assorted applications. Theory and Applications of Graphs, Lecture Notes in Math. 642, (1978), 53-65.
• Miller, J. C. P. Difference bases. Three problems in additive number theory. Computers in number theory (Proc. Sci. Res. Council Atlas Sympos. No. 2, Oxford, 1969), pp. 299--322. Academic Press, London,1971. MR0316269 (47 #4817) - From N. J. A. Sloane, Jun 05 2012
• Rhys Price Jones, Gracelessness, Proc. 10th S.-E. Conf. Combin., Graph Theory and Computing, 1979, pp. 547-552. - From N. J. A. Sloane, Jun 05 2012

Links

• G. S. Bloom and S. W. Golomb, Applications of numbered undirected graphs, Proc. IEEE 65 (1977), 562-570.
• Index entries for sequences related to Golomb rulers

Crossrefs

Cf. A003022, A078106, A004137.

Formula

n(n-1)/2 = a(n)+A004137(n). - Kellen Myers, Jun 06 2016

Extensions

a(26) using extension of A004137 from Hugo Pfoertner, Feb 28 2021