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A076184 Graph code numbers of simple graphs in numerical order. 1


%S 0,1,3,7,11,12,13,15,30,31,63,75,76,77,79,86,87,94,95,116,117,119,127,

%T 222,223,235,236,237,239,254,255,507,511,1023,1099,1100,1101,1103,

%U 1108,1109,1110,1111,1118,1119,1140,1141,1143,1151,1182,1183,1184,1185,1187

%N Graph code numbers of simple graphs in numerical order.

%C 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.

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

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

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

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

%H Vladimir Kulipanov, <a href="/A076184/a076184.txt">Table of n, a(n) for n = 1..156</a>

%e 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].

%e 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].

%Y Cf. A000088.

%K nonn

%O 1,3

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

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