A076184 Graph code numbers of simple graphs in numerical order.

0, 1, 3, 7, 11, 12, 13, 15, 30, 31, 63, 75, 76, 77, 79, 86, 87, 94, 95, 116, 117, 119, 127, 222, 223, 235, 236, 237, 239, 254, 255, 507, 511, 1023, 1099, 1100, 1101, 1103, 1108, 1109, 1110, 1111, 1118, 1119, 1140, 1141, 1143, 1151, 1182, 1183, 1184, 1185, 1187

Offset

1,3

Comments

Every simple graph has a symmetric adjacency matrix whose lower triangular part by rows represents a little-endian binary number of which the minimum value over all isomorphic graphs gives the graph code number. Adding isolated vertices will not change the graph code number.

Study of the patterns and gaps in the sequence appears to be quite interesting.

The number of terms that are less than 2^(n*(n-1)/2) is equal to A000088(n). - Vladimir Kulipanov, Oct 13 2015

References

F. Harary, Problems involving graphical numbers, in Colloq. Math. Soc. Janos Bolyai, 4 (1970) 625-635. Look at his 'mincode numbers'.

K. R. Parthasarathy, Graph Code Numbers, preprint.

Links

Table of n, a(n) for n=1..53.

Vladimir Kulipanov, Table of n, a(n) for n = 1..156

Example

a(5)=11 in binary (with 0's prepended to give a triangular number of digits) is 001011 so adjacency matrix [0,1,1,1; 1,0,0,0; 1,0,0,0; 1,0,0,0].
a(6)=12 in binary is 001100 so adjacency matrix [0,0,0,1; 0,0,1,0; 0,1,0,0; 1,0,0,0].

Crossrefs

Cf. A000088.

Sequence in context: A337250 A043345 A023718 * A310191 A135137 A263737

Adjacent sequences: A076181 A076182 A076183 * A076185 A076186 A076187

Keyword

nonn

Author

K. R. Parthasarathy (nuns(AT)vsnl.com), Nov 02 2002

Status

approved