A299030 Number of vertices in the iterated clique graphs of the 1-skeleton of Plato's octahedron.

6, 8, 16, 256, 340282366920938463463374607431768211456

Offset: 0

Author

José Hernández, Feb 01 2018

Keywords

• nonn
• more

Comments

The octahedron was the first known example of a k-divergent graph.

Examples

			By definition, the zeroth iterated clique graph of a graph G is equal to G itself; since the octahedron has 6 vertices, a(0)=6.
The first iterated clique graph of the octahedron has 8 vertices; hence, a(1)=8.
		

Links

• Miguel A. Pizaña, The icosahedron is clique divergent, Discrete Mathematics, 262 (Feb. 2003), pp. 229-239.
• YAGS, YAGS - Yet Another Graph System

Crossrefs

Cf. A299028, A063723, A053016.

Programs

Mathematica

Nest[Sqrt[2]^#&, 6, n] (* Omar Antolín-Camarena, May 16 2022 *)

YAGS

K:=CliqueGraph;; g:=Octahedron;; kg:=K(g);; Order(kg);
# It outputs the number of vertices in the first iterated
# clique graph of the octahedron.

Formula

a(n) = sqrt(2)^sqrt(2)^...^sqrt(2)^6 with n occurrences of sqrt(2). - Omar Antolín-Camarena, May 16 2022

Extensions

a(4) from Omar Antolín-Camarena, May 16 2022