A156809
Number of nonisomorphic circle graphs of order n.
Original entry on oeis.org
1, 2, 4, 11, 34, 154, 978, 9497, 127954, 2165291, 42609994, 937233306, 22576188846
Offset: 1
Lars Eirik Danielsen (larsed(AT)ii.uib.no), Feb 16 2009
- R. Arratia, B. Bollobas, D. Coppersmith, and G. B. Sorkin, Euler circuits and DNA sequencing by hybridization, Discrete Appl. Math., 104 (2000), 63-96.
- Gi-Sang Cheon, Jinha Kim, Minki Kim, Sergey Kitaev, On k-11-representable graphs, arXiv:1803.01055 [math.CO], 2018.
- L. E. Danielsen and M. G. Parker, Interlace polynomials: Enumeration, unimodality, and connections to codes, arXiv:0804.2576 [math.CO], 2008-2009.
- L. E. Danielsen, Database of Circle Graphs.
A319489
Number of non-isomorphic connected graphs on n vertices with representation number 2.
Original entry on oeis.org
0, 0, 1, 5, 20, 109, 788, 8335, 117282, 2026330, 40302424, 892278075
Offset: 1
For n=3 there is one connected graph with vertex set, say, {1,2}, which is represented by 1212.
Equals
A156808 minus 1; graphs with representation number 3 are in
A319490.
A318188
Number of nonisomorphic 2-connected circle graphs of order n.
Original entry on oeis.org
0, 1, 1, 3, 10, 54, 407, 4630, 68425, 1211637
Offset: 1
The 3 circle graphs with n = 4 vertices which are 2-connected are K_4, the square and the square with one diagonal.
- L. E. Danielsen, Database of Circle Graphs
- L. E. Danielsen and M. G. Parker, Interlace polynomials: Enumeration, unimodality, and connections to codes, arXiv:0804.2576 [math.CO], 2008-2009.
- L. E. Danielsen and M. G. Parker, Interlace polynomials: Enumeration, unimodality, and connections to codes, Discrete Appl. Math. 158(6), pp. 636-648, 2010.
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