A303156 -id:A303156 - cp's OEIS frontend

A302401 Total domination number of the n X n king graph.

Original entry on oeis.org

2, 2, 4, 5, 8, 9, 12, 15, 18, 21, 24, 29, 32, 38, 43, 48, 53, 60, 66, 72, 79

Offset: 2

Eric W. Weisstein, Apr 07 2018

Eric Weisstein's World of Mathematics, King Graph
Eric Weisstein's World of Mathematics, Total Domination Number
Eric W. Weisstein, Example minimum total domination configurations for n X n king graphs

Main diagonal of A303378.

Cf. A303156.

a(n) ~ n^2/7. - Andrew Howroyd, Apr 22 2018

a(17)-a(18) from Andrew Howroyd, Apr 22 2018
a(19)-a(20) from Eric W. Weisstein, Sep 09 2021
a(21) from Eric W. Weisstein, Sep 12 2021
a(22) from Eric W. Weisstein, Sep 15 2021

A303335 Array read by antidiagonals: T(m,n) is the number of minimum total dominating sets in the m X n king graph.

Original entry on oeis.org

0, 1, 1, 2, 6, 2, 1, 9, 9, 1, 1, 4, 8, 4, 1, 4, 8, 1, 1, 8, 4, 3, 89, 3, 35, 3, 89, 3, 1, 56, 76, 9, 9, 76, 56, 1, 2, 16, 17, 1, 1, 1, 17, 16, 2, 9, 64, 1, 130, 9, 9, 130, 1, 64, 9, 4, 780, 6, 16, 60, 8684, 60, 16, 6, 780, 4, 1, 304, 229, 1, 89, 493, 493, 89, 1, 229, 304, 1

Offset: 1

Andrew Howroyd, Apr 21 2018

The minimum size of a total dominating set is the total domination number A303378(m, n).

			Table begins:
=========================================
m\n| 1  2  3   4  5    6   7   8    9
---+-------------------------------------
1  | 0  1  2   1  1    4   3   1    2 ...
2  | 1  6  9   4  8   89  56  16   64 ...
3  | 2  9  8   1  3   76  17   1    6 ...
4  | 1  4  1  35  9    1 130  16    1 ...
5  | 1  8  3   9  1    9  60  89   45 ...
6  | 4 89 76   1  9 8684 493   1   50 ...
7  | 3 56 17 130 60  493 208  40   32 ...
8  | 1 16  1  16 89    1  40 604    1 ...
9  | 2 64  6   1 45   50  32   1 1192 ...
...

Andrew Howroyd, Table of n, a(n) for n = 1..435
Eric Weisstein's World of Mathematics, King Graph.
Eric Weisstein's World of Mathematics, Minimum Total Dominating Set.

Rows 1..2 are A302654, A350817.
Main diagonal is A303156.
Cf. A303114, A303293, A303378, A332390, A350815.

A303116 Number of total dominating sets in the n X n king graph.

Original entry on oeis.org

0, 11, 353, 35458, 16322279, 30158547693, 217221533288240, 6223220939472363571, 709791800918008570287847, 321673400252458591521699180612, 579292884621843116328602359172702605, 4146239141804826663870561644604700888044071

Offset: 1

Andrew Howroyd, Apr 18 2018

nonn

Eric Weisstein's World of Mathematics, King Graph
Eric Weisstein's World of Mathematics, Total Dominating Set

Main diagonal of A303114.

Cf. A133791, A302401, A303156, A332391.

A332391 Number of minimal total dominating sets in the n X n king graph.

Original entry on oeis.org

0, 6, 20, 141, 7770, 204372, 16260853, 4570906041, 1437642613959, 1151580438927120

Offset: 1

Andrew Howroyd, Feb 10 2020

Eric Weisstein's World of Mathematics, King Graph.
Eric Weisstein's World of Mathematics, Minimal Total Dominating Set.

Main diagonal of A332390.

Cf. A302401, A303116, A303156.

a(9)-a(10) from Christian Sievers, Dec 02 2023

cp's OEIS Frontend

A302401 Total domination number of the n X n king graph.

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions

A303335 Array read by antidiagonals: T(m,n) is the number of minimum total dominating sets in the m X n king graph.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A303116 Number of total dominating sets in the n X n king graph.

Views

Author

Keywords

Links

Crossrefs

A332391 Number of minimal total dominating sets in the n X n king graph.

Views

Author

Keywords

Links

Crossrefs

Extensions