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Number of non-isomorphic connected graphs on n vertices with representation number 3.

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`%I #11 Sep 28 2018 10:17:00
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`%S 0,0,0,0,0,1,39,1852,88838
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`%N Number of non-isomorphic connected graphs on n vertices with representation number 3.
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`%C These are graphs that can be represented by words having three copies of each letter, but cannot be represented by words having two copies of each letter. In a word representing a graph G, letters x and y alternate if any only if there is an edge between x and y in G.
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`%H Ozgur Akgun, Ian P. Gent, Sergey Kitaev, Hans Zantema, <a href="https://arxiv.org/abs/1808.01215">Solving computational problems in the theory of word-representable graphs</a>, arXiv:1808.01215 [math.CO], 2018.
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`%H Sergey Kitaev, <a href="https://arxiv.org/abs/1705.05924">A comprehensive introduction to the theory of word-representable graphs</a>, arXiv:1705.05924 [math.CO], 2017.
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`%e The triangular prism is the only graph on 6 vertices that can be represented using three copies of each letter, but cannot be represented using 2 copies of each letter.
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`%Y Cf. A319489 (graphs with representation number 2).
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`%K nonn,more
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`%O 1,7
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`%A _Sergey Kitaev_, Sep 20 2018
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