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%I #28 Oct 24 2023 23:14:54
%S 1,0,0,0,1,4,24,191,3094,95204,5561965
%N Number of simplicial-free connected simple graphs on n unlabeled vertices.
%C A simplicial vertex is one whose neighborhood induces a complete graph. A simplicial-free graph has no such vertices.
%H Chı́nh. T Hoàng, Stefan Hougardy, Frédéric Maffray and N.V.R. Mahadev, <a href="https://doi.org/10.1016/S0166-218X(03)00275-0">On simplicial and co-simplicial vertices in graphs</a>, Discrete Applied Mathematics 138, (2004) 117-132.
%H Andrew M. Steane, <a href="https://arxiv.org/abs/1210.7985">Threat, support and dead edges in the Shannon game</a>, arXiv:1210.7985 [math.CO], 2012.
%e For n=0 the graph with no vertices has no simplicial vertices so a(0)=1.
%e For n=4 the only case is C4 so a(4)=1.
%e For n=5 the a(5)=4 solutions are C5 and the graphs obtained by adding to C4 a further vertex adjacent to either 4,3 or 2 of the others, in the latter case without forming a triangle:
%e o o o
%e /|\ /|\ /|\
%e o o o o-o-o o-o-o
%e \|/ \ / \|/
%e o o o
%K nonn,more
%O 0,6
%A _Andrew M. Steane_, Oct 08 2023
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