A287024 Triangle read by rows: T(n,k) is the number of graphs with n vertices with vertex cover number k-1.

1, 1, 1, 1, 2, 1, 1, 3, 6, 1, 1, 4, 15, 13, 1, 1, 5, 30, 82, 37, 1, 1, 6, 51, 301, 578, 106, 1, 1, 7, 80, 842, 4985, 6021, 409, 1, 1, 8, 117, 1995, 27107, 142276, 101267, 1896, 1, 1, 9, 164, 4210, 112225, 1724440, 7269487, 2882460, 12171, 1, 1, 10, 221, 8165, 388547, 13893557, 210799447, 655015612, 138787233, 105070, 1

Offset: 1

Author

Eric W. Weisstein, May 18 2017

Keywords

• nonn
• tabl

Comments

Aside from trailing 1's, same as A115196.

Examples

			Triangle begins:
  1;
  1, 1;
  1, 2,   1;
  1, 3,   6,    1;
  1, 4,  15,   13,      1;
  1, 5,  30,   82,     37,       1;
  1, 6,  51,  301,    578,     106,       1;
  1, 7,  80,  842,   4985,    6021,     409,       1;
  1, 8, 117, 1995,  27107,  142276,  101267,    1896,     1;
  1, 9, 164, 4210, 112225, 1724440, 7269487, 2882460, 12171, 1;
  ...
Row 3 is 1, 2, 1 because
\bar K_3 (1 graph) has vertex cover number 0
K_1\cup K_2 and P_3 (2 graphs) have vertex cover number 1
K_3=C_3 (1 graph) has vertex cover number 2
Here, \bar denotes graph complementation and \cup denotes (disjoint) graph union.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..91 (first 13 rows, after Brendan McKay data in A263341)
• Eric Weisstein's World of Mathematics, Vertex Cover
• Eric Weisstein's World of Mathematics, Vertex Cover Number

Crossrefs

Cf. A000088 (row sums), A115196 (number of graphs on n nodes with clique number k), A263341.

Extensions

Terms a(46) and beyond from Brendan McKay added by Andrew Howroyd, Feb 19 2020