

A111916


Number of Yutsis graphs or cubic dual hamiltonian graphs on 2n nodes.


1



1, 2, 5, 18, 80, 475, 3836, 39555, 495045, 7159696, 116040456, 2068782009, 40107422184, 838931116609
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,2


COMMENTS

Connected cubic graphs on 2n nodes which can be partitioned into two vertex induced trees which are necessarily of the same size.
They are called dual Hamiltonian because the cut separating both trees contains n+2 edges, corresponding to a Hamiltonian cycle in the planar dual if the graph is planar.
Maximal connected cubic graphs in the size of the largest vertex induced forest (floor((6*n2)/4) nodes for a cubic graph on 2n nodes).


REFERENCES

F. Jaeger, On vertexinduced forests in cubic graphs, Proceedings 5th Southeastern Conference, Congressus Numerantium (1974) 501512
D. Van Dyck, G. Brinkmann, V. Fack and B. D. McKay, To be or not to be Yutsis: algorithms for the decision problem', Computer Physics Communications 173 (2005) 6170
A. P. Yutsis, I. B. Levinson and V. V. Vanagas, Mathematical Apparatus of the Theory of Angular Momentum, Israel Program for Scientific Translation, Jerusalem, 1962


LINKS

Table of n, a(n) for n=2..15.
Dries Van Dyck and Veerle Fack, Yutsis Project


CROSSREFS

Sequence in context: A206293 A137861 A192637 * A118187 A038720 A157312
Adjacent sequences: A111913 A111914 A111915 * A111917 A111918 A111919


KEYWORD

nonn


AUTHOR

Dries Van Dyck (VanDyck.Dries(AT)Gmail.com), Mar 05 2006


STATUS

approved



