A387827 Number of fundamentally different graceful labelings of the complement of the n-path graph.

1, 0, 0, 1, 13, 34, 45, 18, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,5

Comments

For n >= 10, the graph has too many edges to have any graceful labelings.

Links

Table of n, a(n) for n=1..86.

Eric Weisstein's World of Mathematics, Graceful Labeling.

Eric Weisstein's World of Mathematics, Path Complement Graph.

Formula

a(n) = 0 for n >= 10.

a(n) = A336428(n)/4 for n > 1.

Crossrefs

Cf. A336428 (all graceful labelings).

Sequence in context: A124659 A164539 A245170 * A134864 A093100 A292472

Adjacent sequences: A387824 A387825 A387826 * A387828 A387829 A387830

Keyword

nonn

Author

Eric W. Weisstein, Sep 09 2025

Status

approved