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 A319489 Number of non-isomorphic connected graphs on n vertices with representation number 2. 1
 0, 0, 1, 5, 20, 109, 788, 8335, 117282, 2026330, 40302424, 892278075 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 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 any 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. LINKS Ozgur Akgun, Ian P. Gent, Sergey Kitaev, 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. EXAMPLE For n=3 there is one connected graph with vertex set, say, {1,2}, which is represented by 1212. CROSSREFS Equals A156808 minus 1; graphs with representation number 3 are in A319490. Sequence in context: A277032 A300490 A020039 * A207972 A117736 A258665 Adjacent sequences:  A319486 A319487 A319488 * A319490 A319491 A319492 KEYWORD nonn,more AUTHOR Sergey Kitaev, Sep 20 2018 STATUS approved

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Last modified October 18 12:18 EDT 2019. Contains 328160 sequences. (Running on oeis4.)