A336428 Total number of graceful labelings of the complement of the path graph P_n.

1, 0, 0, 4, 52, 136, 180, 72, 4, 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

1,4

Comments

For n >= 10, the graph has too many edges to have any graceful labelings. - Eric W. Weisstein, Sep 09 2025

Links

Table of n, a(n) for n=1..85.

Eric Weisstein's World of Mathematics, Graceful Labeling

Eric Weisstein's World of Mathematics, Path Complement Graph

Formula

a(n) = 0 for n >= 10. - Eric W. Weisstein, Sep 09 2025

a(n) = 4*A387827(n) for n > 1. - Eric W. Weisstein, Sep 09 2025

Crossrefs

Cf. A387827 (fundamentally different labelings).

Sequence in context: A329009 A110908 A232507 * A298073 A233474 A297764

Adjacent sequences: A336425 A336426 A336427 * A336429 A336430 A336431

Keyword

nonn,more

Author

Eric W. Weisstein, Jul 21 2020

Extensions

a(11) = 0 and subsequent 0 terms appended by Eric W. Weisstein, Sep 09 2025

Status

approved