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

0,4

Links

Table of n, a(n) for n=0..71.

Formula

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

Example

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.

Sequence in context: A173465 A151837 A356354 * A355339 A331856 A163381

Adjacent sequences: A382278 A382279 A382280 * A382282 A382283 A382284

Keyword

nonn

Author

Pontus von Brömssen, Mar 21 2025

Status

approved