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