A291775 - OEIS

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A291775

Domination number of the n-Sierpinski carpet graph.

3, 18, 130, 1026

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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)

LINKS

Table of n, a(n) for n=1..4.

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

EXAMPLE

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

CROSSREFS

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