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Search: id:A076184
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| A076184 |
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Graph code numbers of simple graphs in numerical order. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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.
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REFERENCES
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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.
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EXAMPLE
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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].
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CROSSREFS
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Sequence in context: A083754 A043345 A023718 this_sequence A135137 A055050 A096346
Adjacent sequences: A076181 A076182 A076183 this_sequence A076185 A076186 A076187
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KEYWORD
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nonn
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AUTHOR
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K. R. Parthasarathy (nuns(AT)vsnl.com), Nov 02 2002
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