A334613 Number of distinct graceful labelings of bipartite graphs with n vertices and n-1 edges.

1, 1, 1, 2, 7, 28, 151, 907, 6467, 51151, 458478, 4455476, 48162974, 557022350, 7020022164, 94129389215, 1357181821028, 20661645476348

Offset: 1

Author

Don Knuth, Sep 08 2020

Keywords

• nonn
• more

Comments

Consider vertices numbered 1 to n. Add the edges 1--n, 2--n, and either 1--(n+1-k), 2--(n+2-k), ... or k--n for 3<=k

Examples

			For example, the seven labelings for n=5 are:
  1--5, 2--5, 1--3, 2--3;
  1--5, 2--5, 1--3, 3--4;
  1--5, 2--5, 1--3, 4--5;
  1--5, 2--5, 2--4, 2--3;
  1--5, 2--5, 2--4, 3--4;
  1--5, 2--5, 3--5, 3--4;
  1--5, 2--5, 3--5, 4--5.
The first of these is the four-cycle plus an isolated vertex; the other six are the trees in A337274.
		

Crossrefs

Cf. A337274.

Extensions

a(17)-a(18) from Bert Dobbelaere, Sep 11 2020

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