OFFSET
0,6
COMMENTS
A simplicial vertex is one whose neighborhood induces a complete graph. A simplicial-free graph has no such vertices.
LINKS
Chı́nh. T Hoàng, Stefan Hougardy, Frédéric Maffray and N.V.R. Mahadev, On simplicial and co-simplicial vertices in graphs, Discrete Applied Mathematics 138, (2004) 117-132.
Andrew M. Steane, Threat, support and dead edges in the Shannon game, arXiv:1210.7985 [math.CO], 2012.
EXAMPLE
For n=0 the graph with no vertices has no simplicial vertices so a(0)=1.
For n=4 the only case is C4 so a(4)=1.
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:
o o o
/|\ /|\ /|\
o o o o-o-o o-o-o
\|/ \ / \|/
o o o
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Andrew M. Steane, Oct 08 2023
STATUS
approved