OFFSET
1,5
COMMENTS
This is the labeled version of A370072. Here, in contrast to A370072, it does not matter which graph we start with.
Define a graph on 2^(n*(n-1)/2) nodes, where each node corresponds to a labeled graph on [n] and two nodes are adjacent if the symmetric difference of the edge sets of the corresponding graphs equals the set of edges of a complete graph on a subset of [n]. This graph is vertex transitive, and T(n,k) is the number of nodes at distance k from a given node. The independence number of this graph is studied in Alon (2024).
LINKS
Noga Alon, Graph-codes, European Journal of Combinatorics 116 (2024), Article ID 103880; arXiv version.
EXAMPLE
Triangle begins:
1;
1, 1;
1, 4, 3;
1, 11, 40, 12;
1, 26, 280, 657, 60;
1, 57, 1491, 13447, 17412, 360;
1, 120, 6930, 178297, 1127388, 781896, 2520;
...
CROSSREFS
KEYWORD
AUTHOR
Pontus von Brömssen, Feb 23 2024
STATUS
approved