A277863 Number of connected, unlabeled, unrooted 3-leaf power graphs on n vertices.

1, 1, 2, 5, 12, 32, 82, 227, 629, 1840, 5456, 16701, 51939, 164688, 529070, 1722271, 5664786, 18813360, 62996841, 212533216, 721792751, 2466135364, 8471967927, 29249059281, 101440962284, 353289339914, 1235154230047, 4333718587339, 15255879756019, 53870521140911

Offset

0,3

Comments

a(n) is the number of unlabeled and unrooted distance-hereditary graphs on n vertices; the enumeration is obtained from the symbolic specification / generating functions through Maple's combstruct library--an arbitrary number of terms can be derived.

Enumeration also exists in various other configurations of unlabeled/labeled, unrooted/rooted, etc.

Links

Table of n, a(n) for n=0..29.

C. Chauve, É. Fusy and J. Lumbroso, An Exact Enumeration of Distance-Hereditary Graphs, arXiv:1608.01464 [math.CO], Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium On Discrete Algorithms, ANALCO session. SIAM (2017).

A. Iriza, Enumeration and random generation of unlabeled classes of graphs: A practical study of cycle pointing and the dissymmetry theorem, arXiv:1511.06037 [cs.DM], Master's Thesis, Princeton University (2015).

A. Iriza, Boltzmann Samplers for unlabeled, unrooted Distance-Hereditary and 3-Leaf Power Graphs.

Graph Classes, 3-leaf power.

Wikipedia, Leaf power.

Wikipedia, Distance-hereditary graph.

Crossrefs

Subset of A277862 (distance-hereditary graphs).

Sequence in context: A265265 A293868 A162434 * A039809 A335456 A345200

Adjacent sequences: A277860 A277861 A277862 * A277864 A277865 A277866

Keyword

nonn,easy

Author

Jérémie Lumbroso, Nov 02 2016

Status

approved