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%I #16 Sep 30 2023 13:07:42
%S 0,0,1,5,20,109,788,8335,117282,2026330,40302424,892278075
%N Number of non-isomorphic connected graphs on n vertices with representation number 2.
%C 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.
%H Ozgur Akgun, Ian P. Gent, Sergey Kitaev, and 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.
%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.
%e For n=3 there is one connected graph with vertex set, say, {1,2}, which is represented by 1212.
%Y Equals A156808 minus 1; graphs with representation number 3 are in A319490.
%K nonn,more
%O 1,4
%A _Sergey Kitaev_, Sep 20 2018
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