A177741 Triangle in which row n lists the numbers of strong vertex magic total labelings of each 2-regular simple graph on 2n+1 vertices.

1, 1, 9, 0, 31, 8, 4, 2, 308, 81, 100, 70, 0, 7, 3809, 578, 474, 495, 454, 103, 181, 103, 97, 0, 63995, 11703, 11655, 9472, 9252, 1151, 8567, 2297, 1758, 1389, 1117, 2023, 104, 328, 210, 128, 11, 1152784, 201685, 193899, 159485, 144516, 19625, 137561, 38453

Offset

1,3

Comments

The 2-regular simple graphs are the disjoint unions of simple cycles (the smallest simple cycle being a triangle).

A simple counting argument shows that no 2-regular graph of even order possesses a strong VMTL.

The ordering of the graphs in row n is the ordering of the corresponding partitions listed in row 2n+1 of A176210.

Links

J. S. Kimberley, Rows 1..9 of A177741 triangle, flattened.

I. D. Gray and J. A. MacDougall, Vertex-magic labelings of regular graphs. II, Discrete Mathematics, 309 (2009), 5986-5999.

Crossrefs

The length of row n is A008483(2n+1).

The row sums are A177742.

The first column is A177743.

Sequence in context: A005066 A076262 A167301 * A182213 A340954 A087094

Adjacent sequences: A177738 A177739 A177740 * A177742 A177743 A177744

Keyword

nonn,tabf

Author

Jason Kimberley, May 17 2010

Status

approved