VOOZH about

URL: https://oeis.org/A392291

⇱ A392291 - OEIS

login
A392291
List of all possible composition numbers of graphs.
4
1, 2, 4, 5, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 27, 30, 31, 32, 34, 35, 38, 40, 43, 47, 48, 50, 52, 54, 58, 60, 62, 64, 65, 68, 69, 70, 74, 75, 76, 79, 80, 81, 83, 86, 87, 89, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 104, 105, 107, 108, 110, 111, 114, 116
OFFSET
1,2
COMMENTS
For a graph G, a graph composition of G is a partition of its vertex set into sets that induce connected subgraphs of G. The composition number of G is the number of graph compositions of G.
All terms are realized by connected graphs, because if two nodes from different components of a graph are identified, the composition number does not change.
Closed under multiplication, because the composition number of the disjoint union of two graphs equals the product of the composition numbers of the two graphs. A392293 gives the primitive terms.
LINKS
Pontus von Brömssen, Table of n, a(n) for n = 1..159
A. Knopfmacher and M. E. Mays, Graph Compositions I: Basic Enumeration, Integers 1 (2001), A4.
CROSSREFS
Cf. A392292 (biconnected graphs), A392293 (primitive terms).
Subsequences include: A000079 (trees), A000110 (complete graphs), A000325 (cycles), A058975 (hypercube graphs), A078468, A110476, A265417 (complete bipartite graphs), A282010, A344638, A346273, A367172, A367173, A367174, A367703, A389996, A389997, A389998.
Sequence in context: A018457 A046809 A112777 * A188972 A047612 A123886
KEYWORD
nonn
AUTHOR
STATUS
approved