A319491 - OEIS

%I #10 Sep 28 2018 10:17:21

%S 0,1,10,47,179

%N Number of minimal non-word-representable connected graphs on n vertices.

%C A simple graph G=(V,E) is word-representable if there exists a word w over the alphabet V such that letters x and y alternate in w iff xy is an edge in E. Word-representable graphs generalize several important classes of graphs.

%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 wheel graph W_5 is the only minimal connected graph on 6 vertices that is not word-representable.

%Y All non-word-representable connected graphs are in A290814.

%K nonn,more

%O 5,3

%A _Sergey Kitaev_, Sep 20 2018