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A076184
Graph code numbers of simple graphs in numerical order.
1
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.
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
KEYWORD
nonn
AUTHOR
K. R. Parthasarathy (nuns(AT)vsnl.com), Nov 02 2002
STATUS
approved