A291775 Domination number of the n-Sierpinski carpet graph.

3, 18, 130, 1026

Offset: 1

Author

Eric W. Weisstein, Aug 31 2017

Keywords

• nonn
• more

Comments

Also the lower independence number (=independent domination number) of the n-Sierpinski carpet graph. - Eric W. Weisstein, Aug 02 2023

From Allan Bickle, Aug 10 2024: (Start)

The level 0 Sierpinski carpet graph is a single vertex. The level n Sierpinski carpet graph is formed from 8 copies of level n-1 by joining boundary vertices between adjacent copies.

Conjecture: For n>1, a(n) = 2^(3n-2) + 2. There is an independent dominating set of this size consisting of the vertices on every third diagonal and two corner vertices.

(End)

Examples

			The 8-cycle has domination number 3, so a(1) = 3.
		

Links

• Allan Bickle, Degrees of Menger and Sierpinski Graphs, Congr. Num. 227 (2016) 197-208.
• Allan Bickle, MegaMenger Graphs, The College Mathematics Journal, 49 1 (2018) 20-26.
• Eric Weisstein's World of Mathematics, Domination Number
• Eric Weisstein's World of Mathematics, Lower Independence Number
• Eric Weisstein's World of Mathematics, Sierpinski Carpet Graph

Crossrefs

Cf. A001018 (order), A271939 (size).

Cf. A365606 (degree 2), A365607 (degree 3), A365608 (degree 4).

Cf. A292707, A347651 (vertex sets).