A319490 - OEIS

%I #11 Sep 28 2018 10:17:00

%S 0,0,0,0,0,1,39,1852,88838

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

%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.

%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.

%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 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.

%Y Cf. A319489 (graphs with representation number 2).

%K nonn,more

%O 1,7

%A _Sergey Kitaev_, Sep 20 2018