login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A263284 Triangle read by rows: T(n,k) is the number of graphs on n vertices with domination number k. 9
1, 1, 1, 2, 1, 1, 4, 5, 1, 1, 11, 16, 5, 1, 1, 34, 94, 21, 5, 1, 1, 156, 708, 152, 21, 5, 1, 1, 1044, 9384, 1724, 166, 21, 5, 1, 1, 12346, 221135, 38996, 1997, 166, 21, 5, 1, 1, 274668, 9877969, 1800340, 49961, 2036, 166, 21, 5, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
The domination number of a graph is given by the minimum size of a dominating set of vertices. A dominating set of vertices is a subset of the vertex set of such that every vertex is either in this subset or adjacent to an element of this subset.
For any graph the domination number is greater than or equal to the irredundance number (A332404) and less than or equal to the independent domination number (A332402). - Andrew Howroyd, Feb 13 2020
LINKS
FindStat - Combinatorial Statistic Finder, The domination number of a graph.
Eric Weisstein's World of Mathematics, Domination Number
FORMULA
T(n,k) = T(n-1,k-1) for 2*(k-1) >= n. - Andrew Howroyd, Feb 17 2020
EXAMPLE
Triangle begins:
1;
1, 1;
2, 1, 1;
4, 5, 1, 1;
11, 16, 5, 1, 1;
34, 94, 21, 5, 1, 1;
156, 708, 152, 21, 5, 1, 1;
1044, 9384, 1724, 166, 21, 5, 1, 1;
12346, 221135, 38996, 1997, 166, 21, 5, 1, 1;
274668, 9877969, 1800340, 49961, 2036, 166, 21, 5, 1, 1;
...
CROSSREFS
Row sums are A000088.
Columns k=1..2 are A000088(n-1), A332625.
Sequence in context: A291261 A294206 A332402 * A332404 A308905 A158471
KEYWORD
nonn,tabl,more
AUTHOR
Christian Stump, Oct 13 2015
EXTENSIONS
Extended to 10 rows by Eric W. Weisstein, May 18 2017
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 12 20:38 EDT 2024. Contains 371639 sequences. (Running on oeis4.)