A243013 - OEIS

%I #6 May 31 2014 21:30:19

%S 1,1,1,3,5,12,36

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

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

%e 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: ∆ / .

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

%K more,nonn

%O 1,4

%A _Gordon Hamilton_, May 28 2014