cp's OEIS Frontend

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

%I A287024 #26 Feb 16 2025 08:33:46
%S A287024 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,
%T A287024 1,7,80,842,4985,6021,409,1,1,8,117,1995,27107,142276,101267,1896,1,1,
%U A287024 9,164,4210,112225,1724440,7269487,2882460,12171,1,1,10,221,8165,388547,13893557,210799447,655015612,138787233,105070,1
%N A287024 Triangle read by rows: T(n,k) is the number of graphs with n vertices with vertex cover number k-1.
%C A287024 Aside from trailing 1's, same as A115196.
%H A287024 Andrew Howroyd, <a href="/A287024/b287024.txt">Table of n, a(n) for n = 1..91</a> (first 13 rows, after Brendan McKay data in A263341)
%H A287024 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VertexCover.html">Vertex Cover</a>
%H A287024 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VertexCoverNumber.html">Vertex Cover Number</a>
%e A287024 Triangle begins:
%e A287024   1;
%e A287024   1, 1;
%e A287024   1, 2,   1;
%e A287024   1, 3,   6,    1;
%e A287024   1, 4,  15,   13,      1;
%e A287024   1, 5,  30,   82,     37,       1;
%e A287024   1, 6,  51,  301,    578,     106,       1;
%e A287024   1, 7,  80,  842,   4985,    6021,     409,       1;
%e A287024   1, 8, 117, 1995,  27107,  142276,  101267,    1896,     1;
%e A287024   1, 9, 164, 4210, 112225, 1724440, 7269487, 2882460, 12171, 1;
%e A287024   ...
%e A287024 Row 3 is 1, 2, 1 because
%e A287024 \bar K_3 (1 graph) has vertex cover number 0
%e A287024 K_1\cup K_2 and P_3 (2 graphs) have vertex cover number 1
%e A287024 K_3=C_3 (1 graph) has vertex cover number 2
%e A287024 Here, \bar denotes graph complementation and \cup denotes (disjoint) graph union.
%Y A287024 Cf. A000088 (row sums), A115196 (number of graphs on n nodes with clique number k), A263341.
%K A287024 nonn,tabl
%O A287024 1,5
%A A287024 _Eric W. Weisstein_, May 18 2017
%E A287024 Terms a(46) and beyond from _Brendan McKay_ added by _Andrew Howroyd_, Feb 19 2020