cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A333728 Maximum number of graceful labelings for a simple graph on n nodes.

Original entry on oeis.org

1, 2, 12, 48, 168, 1152, 9600, 97920
Offset: 1

Views

Author

Eric W. Weisstein, Apr 03 2020

Keywords

Comments

a(9) >= 1491840 (K_1,1,7).
Table of graphs achieving these maxima:
1: K_1
2: K_2 = P_2
3: K_3 = C_3 = K_1,1,1
4: K_4
5: K_1,1,3
6: K_1,1,4
7: K_1,1,5
8: K_1,1,6
a(4) fails to correspond to the diamond graph K_1,1,2 since K_4 has 48 graceful labelings, while K_1,1,2 has only 32.

Crossrefs

Cf. A334307, A339892.

Extensions

a(8) from Eric W. Weisstein, Jul 30 2020

A379395 Maximum number of fundamentally different graceful labelings for a simple graph of n nodes.

Original entry on oeis.org

1, 1, 1, 5, 26, 126, 680, 3876
Offset: 1

Views

Author

Eric W. Weisstein, Dec 22 2024

Keywords

Comments

The difference between "fundamentally different graceful labelings" of a graph and "graceful labelings" of a graph is that the latter is the former multiplied by twice the number of automorphisms. (The extra factor of 2 comes from complementation.)
a(9) >= 25501. - Eric W. Weisstein, Mar 30 2025

Links

Crossrefs

Cf. A339892 (maximum number of fundamentally different graceful labelings excluding graphs with isolated vertices).
Showing 1-2 of 2 results.

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