A382281 Let n encode the edges of a graph by taking edges (u,v), with u < v, in colexicographic order ((0,1), (0,2), (1,2), (0,3), ...) and adding each edge to the graph if the corresponding binary digit of n (starting with the least significant digit) is 1. a(n) is the smallest nonnegative integer that encodes the same unlabeled graph as n (disregarding any isolated vertices), i.e., the code of the graph as defined in A076184.

0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 11, 12, 13, 13, 15, 1, 3, 12, 13, 3, 11, 13, 15, 3, 7, 13, 15, 13, 15, 30, 31, 1, 12, 3, 13, 3, 13, 11, 15, 3, 13, 7, 15, 13, 30, 15, 31, 3, 13, 13, 30, 7, 15, 15, 31, 11, 15, 15, 31, 15, 31, 31, 63, 1, 3, 3, 11, 12, 13, 13, 15

Offset: 0

Author

Pontus von Brömssen, Mar 21 2025

Keywords

• nonn

Examples

			n = 6 is 110 in binary, encoding the graph with edges (0,2) and (1,2), i.e., the path graph on 3 vertices. The canonical code of that graph is a(6) = 3, corresponding to the graph with edges (0,1) and (0,2).
		

Crossrefs

Cf. A076184.

Formula

a(n) <= n with equality if and only if n is in A076184.