cp's OEIS Frontend

A291775 Domination number of the n-Sierpinski carpet graph.

%I A291775 #13 Feb 16 2025 08:33:51
%S A291775 3,18,130,1026
%N A291775 Domination number of the n-Sierpinski carpet graph.
%C A291775 Also the lower independence number (=independent domination number) of the n-Sierpinski carpet graph. - _Eric W. Weisstein_, Aug 02 2023
%C A291775 From _Allan Bickle_, Aug 10 2024: (Start)
%C A291775 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.
%C A291775 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.
%C A291775 (End)
%H A291775 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/mengerspongedegree.pdf">Degrees of Menger and Sierpinski Graphs</a>, Congr. Num. 227 (2016) 197-208.
%H A291775 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/mengerspongeshort.pdf">MegaMenger Graphs</a>, The College Mathematics Journal, 49 1 (2018) 20-26.
%H A291775 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominationNumber.html">Domination Number</a>
%H A291775 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LowerIndependenceNumber.html">Lower Independence Number</a>
%H A291775 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiCarpetGraph.html">Sierpinski Carpet Graph</a>
%e A291775 The 8-cycle has domination number 3, so a(1) = 3.
%Y A291775 Cf. A001018 (order), A271939 (size).
%Y A291775 Cf. A365606 (degree 2), A365607 (degree 3), A365608 (degree 4).
%Y A291775 Cf. A292707, A347651 (vertex sets).
%K A291775 nonn,more
%O A291775 1,1
%A A291775 _Eric W. Weisstein_, Aug 31 2017