A319490 -id:A319490 - cp's OEIS frontend

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

Sergey Kitaev, Sep 20 2018

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.

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

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.

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

cp's OEIS Frontend

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

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