A364208 a(n) is the number of full graphs on n unlabeled vertices (see comments for definition of full graph).

1, 1, 2, 3, 10, 32, 154, 1037, 12339, 274640

Offset

1,3

Comments

Full graphs are defined as follows: A tree T with n vertices is bipartite, let its parts be of size k and n - k with k <= n-k, we rename T as T_k and we say it has type (k, n - k). If a graph G has a spanning tree T_k of type (k,n-k) for each k such that 1 <= k <= [n/2], then we say that G is full.

Full graphs will be featured in an upcoming article by Jayasooriya, McSorley, and Schuerger.

Links

Table of n, a(n) for n=1..10.

Sean A. Irvine, Java program (github)

Example

a(4)=3 as follows. Of the eleven nonisomorphic graphs on four vertices, only four of them contain a subgraph isomorphic to K_{1,3}, and thus a spanning tree of type (1,3).  One of these four graphs does not contain a spanning tree of type (2,2), while the other three graphs each contain a Hamiltonian path and thus a spanning tree of type (2,2).

Crossrefs

Sequence in context: A209003 A080022 A192913 * A358895 A057146 A344573

Adjacent sequences: A364205 A364206 A364207 * A364209 A364210 A364211

Keyword

nonn,more

Author

Houston Schuerger, Aug 26 2023

Extensions

a(8)-a(10) from Sean A. Irvine, Oct 07 2023

Status

approved