|
%I #25 Jun 30 2018 15:32:21
%S 1,1,2,6,18,73,308,1484,7492,40010,220676,1253940,7282316,43096792,
%T 259019070,1577653196,9720170360,60492629435,379820431422,
%U 2403679290621,15319255038074,98255642978084,633833391637128,4110221883283079,26781322507739916,175268504233782739
%N Number of connected, unlabeled, unrooted distance-hereditary graphs on n vertices.
%C 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.
%H H.-J. Bandelt and H. M. Mulder, <a href="http://dx.doi.org/10.1016/0095-8956(86)90043-2">Distance-hereditary graphs</a>, Journal of Combinatorial Theory, Series B, 41 (2): 182-208, doi:10.1016/0095-8956(86)90043-2, MR 0859310 (1986).
%H C. Chauve, É. Fusy and J. Lumbroso, <a href="https://arxiv.org/abs/1608.01464">An Exact Enumeration of Distance-Hereditary Graphs</a>, arXiv:1608.01464 [math.CO], Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium On Discrete Algorithms, ANALCO session. SIAM (2017).
%H E. Howorka, <a href="http://qjmath.oxfordjournals.org/content/28/4/417.extract">A characterization of distance-hereditary graphs</a>, The Quarterly Journal of Mathematics. Oxford. Second Series, 28 (112): 417-420, doi:10.1093/qmath/28.4.417, MR 0485544 (1977).
%H A. Iriza, <a href="https://arxiv.org/abs/1511.06037">Enumeration and random generation of unlabeled classes of graphs: A practical study of cycle pointing and the dissymmetry theorem</a>, arXiv:1511.06037 [cs.DM], Master's Thesis, Princeton University (2015).
%H A. Iriza, <a href="https://github.com/alexiriza/unlabeled-graph-samplers">Boltzmann Samplers for unlabeled, unrooted Distance-Hereditary and 3-Leaf Power Graphs</a>.
%H Jessica Shi, <a href="https://www.cs.princeton.edu/sites/default/files/uploads/jessica_shi.pdf">Enumeration of unlabeled graph classes: A study of tree decompositions and related approaches</a>, 2015.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Distance-hereditary_graph">Distance-Hereditary Graph</a>.
%Y Cf. A280766.
%K nonn,easy
%O 1,3
%A _Jérémie Lumbroso_, Nov 02 2016
%E Offset corrected by _Falk Hüffner_, Jun 27 2018
|
