This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A076184 #39 Mar 19 2025 11:51:38 %S A076184 0,1,3,7,11,12,13,15,30,31,63,75,76,77,79,86,87,94,95,116,117,119,127, %T A076184 222,223,235,236,237,239,254,255,507,511,1023,1099,1100,1101,1103, %U A076184 1108,1109,1110,1111,1118,1119,1140,1141,1143,1151,1182,1183,1184,1185,1187 %N A076184 Graph code numbers of simple graphs in numerical order. %C A076184 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 A076184 Study of the patterns and gaps in the sequence appears to be quite interesting. %C A076184 The number of terms that are less than 2^(n*(n-1)/2) is equal to A000088(n). - _Vladimir Kulipanov_, Oct 13 2015 %C A076184 The numbers of vertices and edges of the graph with code a(n) are A002024(A029837(a(n)+1)) + 1 and A000120(a(n)), respectively. - _Pontus von Brömssen_, Mar 15 2025 %C A076184 To obtain all unlabeled graphs with n vertices (including graphs with isolated vertices), take the graphs associated with the first A000088(n) terms and add isolated vertices so that each graph gets n vertices. - _Pontus von Brömssen_, Mar 19 2025 %D A076184 F. Harary, Problems involving graphical numbers, in Colloq. Math. Soc. Janos Bolyai, 4 (1970) 625-635. Look at his 'mincode numbers'. %H A076184 Pontus von Brömssen, <a href="/A076184/b076184.txt">Table of n, a(n) for n = 1..12346</a> (for graphs on up to 8 vertices; terms 1..156 from Vladimir Kulipanov) %H A076184 Pontus von Brömssen, <a href="/A076184/a076184.py.txt">Python function to convert a code to a list of edges</a>. %H A076184 K. R. Parthasarathy, <a href="https://ssrn.com/abstract=3142728">Graph code numbers</a>, preprint, 2002. %e A076184 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 A076184 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 A076184 Cf. A000088, A000120, A002024, A029837. %K A076184 nonn %O A076184 1,3 %A A076184 K. R. Parthasarathy (nuns(AT)vsnl.com), Nov 02 2002