A243013 Number of graphs with n vertices and n-1 edges that can be gracefully labeled.

1, 1, 1, 3, 5, 12, 36

Offset

1,4

Comments

Hand calculated by grade 3 students up to term 6: (1,1,1,3,5,12...)

Links

Table of n, a(n) for n=1..7.

Example

a(5) = 5: A001433 tells us that there are 6 simple graphs with 5 vertices and 4 edges.  Only 5 of these can be labeled gracefully.  The one that cannot is the triangular loop plus two connected nodes: ∆ / .

Crossrefs

A001433 provides an upper bound. If the Graceful Tree Conjecture were true, A000055 would be a lower bound.

Sequence in context: A220832 A323270 A087610 * A191636 A267337 A308544

Adjacent sequences: A243010 A243011 A243012 * A243014 A243015 A243016

Keyword

more,nonn

Author

Gordon Hamilton, May 28 2014

Status

approved