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A277862 Number of connected, unlabeled, unrooted distance-hereditary graphs on n vertices. 3
1, 1, 2, 6, 18, 73, 308, 1484, 7492, 40010, 220676, 1253940, 7282316, 43096792, 259019070, 1577653196, 9720170360, 60492629435, 379820431422, 2403679290621, 15319255038074, 98255642978084, 633833391637128, 4110221883283079, 26781322507739916, 175268504233782739 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..26.

H.-J. Bandelt and H. M. Mulder, Distance-hereditary graphs, Journal of Combinatorial Theory, Series B, 41 (2): 182-208, doi:10.1016/0095-8956(86)90043-2, MR 0859310 (1986).

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).

E. Howorka, A characterization of distance-hereditary graphs, The Quarterly Journal of Mathematics. Oxford. Second Series, 28 (112): 417-420, doi:10.1093/qmath/28.4.417, MR 0485544 (1977).

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.

Jessica Shi, Enumeration of unlabeled graph classes: A study of tree decompositions and related approaches, 2015.

Wikipedia, Distance-Hereditary Graph.


Cf. A280766.

Sequence in context: A194088 A022491 A004395 * A213427 A006388 A007116

Adjacent sequences:  A277859 A277860 A277861 * A277863 A277864 A277865




Jérémie Lumbroso, Nov 02 2016


Offset corrected by Falk Hüffner, Jun 27 2018



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Last modified October 1 04:05 EDT 2022. Contains 357134 sequences. (Running on oeis4.)