A319489 Number of non-isomorphic connected graphs on n vertices with representation number 2.

0, 0, 1, 5, 20, 109, 788, 8335, 117282, 2026330, 40302424, 892278075

Offset: 1

Author

Sergey Kitaev, Sep 20 2018

Keywords

• nonn
• more

Comments

These are graphs that can be represented by words having two copies of each letter, but cannot be represented by words having one copy of each letter. In a word representing a graph G, letters x and y alternate if and only if there is an edge between x and y in G. Such graphs, along with complete graphs, are precisely the class of circle graphs.

Examples

			For n=3 there is one connected graph with vertex set, say, {1,2}, which is represented by 1212.
		

Links

• Ozgur Akgun, Ian P. Gent, Sergey Kitaev, and Hans Zantema, Solving computational problems in the theory of word-representable graphs, arXiv:1808.01215 [math.CO], 2018.
• Sergey Kitaev, A comprehensive introduction to the theory of word-representable graphs, arXiv:1705.05924 [math.CO], 2017.

Crossrefs

Equals A156808 minus 1; graphs with representation number 3 are in A319490.