

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
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OFFSET

1,3


COMMENTS

Every simple graph has a symmetric adjacency matrix whose lower triangular part by rows represents a littleendian 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.


REFERENCES

F. Harary, Problems involving graphical numbers, in Colloq. Math. Soc. Janos Bolyai, 4 (1970) 625635. Look at his 'mincode numbers'.
K. R. Parthasarathy, Graph Code Numbers, preprint.


LINKS



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



KEYWORD

nonn


AUTHOR

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


STATUS

approved



