A382754
List of unlabeled simple graphs, encoded as integers (see comments).
Original entry on oeis.org
0, 1, 2, 3, 8, 9, 11, 15, 64, 65, 67, 71, 75, 76, 77, 79, 94, 95, 127, 1024, 1025, 1027, 1031, 1039, 1043, 1044, 1045, 1047, 1052, 1053, 1055, 1078, 1079, 1082, 1083, 1086, 1087, 1150, 1151, 1207, 1208, 1209, 1211, 1215, 1231, 1244, 1245, 1247, 1278, 1279, 1519, 1535, 2047
Offset: 0
As an irregular triangle, where row n >= 0 contains A000088(n) terms:
0;
1;
2, 3;
8, 9, 11, 15;
64, 65, 67, 71, 75, 76, 77, 79, 94, 95, 127;
...
71 is a term, because it is the code of the claw graph. If the edges are taken to be (0,1), (0,2), and (0,3), an optimal permutation of the vertices of the graph is (3, 2, 1, 0), with the lower triangular part of the corresponding adjacency matrix being [0; 0,0; 1,1,1]. Adding 2^(4*3/2) to the binary number 000111, we obtain that the code of the claw graph is 64+7 = 71.
Cf.
A000088,
A000120,
A000523,
A002024,
A076184,
A382755,
A382756,
A382757,
A382758,
A382759,
A382760,
A382761,
A382762,
A382763,
A382764.
A382762
List of graphs that are squares, encoded by their indices in A382754.
Original entry on oeis.org
0, 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 17, 18, 19, 20, 24, 25, 32, 39, 40, 47, 49, 51, 52, 53, 54, 59, 60, 70, 89, 90, 99, 107, 117, 127, 144, 160, 170, 171, 172, 177, 182, 186, 191, 193, 195, 201, 204, 205, 206, 207, 208
Offset: 0
As an irregular triangle, where row n >= 0 contains A382181(n) terms:
0;
1;
2, 3;
4, 5, 7;
8, 9, 12, 13, 17, 18;
19, 20, 24, 25, 32, 39, 40, 47, 49, 51, 52;
...
A382763
a(n) is the code (in the encoding given by A382754) of the square of the graph with code A382754(n).
Original entry on oeis.org
0, 1, 2, 3, 8, 9, 15, 15, 64, 65, 75, 127, 75, 76, 95, 127, 127, 127, 127, 1024, 1025, 1043, 1207, 2047, 1043, 1044, 1079, 1207, 1208, 1279, 2047, 1207, 1207, 1247, 1535, 1535, 2047, 2047, 2047, 1207, 1208, 1279, 1535, 2047, 2047, 2047, 2047, 2047, 2047, 2047, 2047, 2047, 2047
Offset: 0
As an irregular triangle, where row n >= 0 contains A000088(n) terms:
0;
1;
2, 3;
8, 9, 15, 15;
64, 65, 75, 127, 75, 76, 95, 127, 127, 127, 127;
...
Showing 1-3 of 3 results.
Comments