来自在线整数百科全书的问候语!搜索:ID:A026624*,在n-超立方体图qnn.c%a027 624中,1n-1的1×i %A027 624、2、3、7、3573252544、1976、88、32、143、3、N、A027、624的独立顶点集的数目也为qnn-α-Er.W.WeiStistin,Join 04 2014 2014 %C A027 624 A. Sapozhenko的顶点覆盖数证明了A(n)~2×SqRT(E)* 2 ^(2 ^(n-1))。http://oei.org/i参见链接(高尔文,2006)。2月11日Ni超立方体图Qyn的最大独立顶点集(顶点独立数)的基数为n=0, 2(n-1),对于n>=1的2015个独立的顶点集(顶点独立数)的基数为1。一个顶点着色,具有着色数2,qqn.-dniel-FuguSez,2月11日2015,FEB 16-17,2015πC A027 624,Qqn的独立顶点对的数目,n>=1:2(n-1)*(2 ^ n-(n+1))=t^(2 ^ n- 1)-n*2 ^(n-1)=Lyn -enn=a00 616(n)-a00 178n(n),其中Lyn是顶点对的数目,Eyn是产生边缘的顶点对的数目。除了n=0之外,有两个这样的集合(其元素具有二进制标记,它们是彼此的位互补)。G.F.为2×2(/(1-2x)^ 2(1-4x))。(A000 0431(n+1),n> 1)- 2月17日,2015πA027 624的独立顶点集的数目为2 ^(n-1)-1项,qqn:2 ^ n=0%C a027 624 2 *(2 ^(n-1)选择2 ^(n-1)-1)。- _Daniel Forgues_, Feb 18 2015 %C A027624 _Daniel Forgues_, Feb 19 2015 (with help from _Robert Israel_): (Start) %C A027624 Number of vertices: 0 1 2 3 4 5 6 7 8 %C A027624 a(0) = 2 = sum(1, 1) %C A027624 a(1) = 3 = sum(1, 2) %C A027624 a(2) = 7 = sum(1, 4, 2) %C A027624 a(3) = 35 = sum(1, 8, 16, 8, 2) %C A027624 a(4) = 743 = sum(1, 16, 88, 208, 228, 128, 56, 16, 2) %C A027624 a(5) = 254475 = sum(1, 32, 416, 2880, 11760, 29856, 48960, 54304, 44240, 29920, 17952, 9088, 3672, 1120, 240, 32, 2) (End) %D A027624 David Galvin, Independent sets in the discrete hypercube, arXiv preprint arXiv:1901.0199, January 2019 [_N. J. A. Sloane_, Apr 29 2019] %D A027624 Ilinca, Liviu, and Jeff Kahn. "计数最大反链和独立集.“30.2阶(2013):427~435.0%H A027 624 David Galvin,离散超立方体中的独立集,2006。%H H A027 624 QuoRA,“n-超立方体图qnn中的独立顶点集数”的序列a027 624是什么意思?Eric Weisstein数学世界,超立方体图Eric Weisstein数学世界,独立顶点集Eric Weisstein数学世界,顶点覆盖%e A027 624 A(0)=2,因为{}和{ 0 }是qy0的独立顶点集,它是由一个标记为0的π.1的顶点组成的图,因为QQ1=0,1有独立的顶点集{},{0 },{1 }。图G的顶点覆盖:G的顶点子集(至多)。at least) one vertex represent an edge of G. %e A027624 Vertices of Q_n are adjacent if and only if a single digit differs in the binary representation of their labels, ranging from 0 to 2^n - 1. %e A027624 a(2) = 7 since Q_2 is %e A027624 00---01 %e A027624 | | %e A027624 10---11 %e A027624 with vertex adjacency submatrix M_2 = %e A027624 M_1 %e A027624 I_2 M_1 %e A027624 for 0 <= i <= 3 and 0 <= j < i %e A027624 00 01 10 11 %e A027624 ___________ %e A027624 00 | %e A027624 01 | 1 %e A027624 10 | 1 0 %e A027624 11 | 0 1 1 %e A027624 yielding the 1 + 4 trivial: { } and {00}, {01}, {10}, {11}; %e A027624 the 2 (= 0 + (4 - 2) + 0) pairs with adjacency 0: {10, 01}, {11, 00}; %e A027624 for a total of 7 = 1 + 2^2 + 2 independent vertex sets. %e A027624 a(3) = 35 since Q_3 is %e A027624 000---------001 %e A027624 | \ / | %e A027624 | 100---101 | %e A027624 | | | | %e A027624 | 110---111 | %e A027624 | / \ | %e A027624 010---------011 %e A027624 with vertex adjacency submatrix M_3 = %e A027624 M_2 %e A027624 I_4 M_2 %e A027624 for 0 <= i <= 7 and 0 <= j < i %e A027624 000 001 010 011 100 101 110 111 %e A027624 ________________________________ %e A027624 000 | %e A027624 001 | 1 %e A027624 010 | 1 0 %e A027624 011 | 0 1 1 %e A027624 100 | 1 0 0 0 %e A027624 101 | 0 1 0 0 1 %e A027624 110 | 0 0 1 0 1 0 %e A027624 111 | 0 0 0 1 0 1 1 %e A027624 yielding the 1 + 8 trivial: { } and %e A027624 {000}, {001}, {010}, {011}, {100}, {101}, {110}, {111}; %e A027624 the 16 (= 2 + (16 - 4) + 2) pairs with adjacency 0: %e A027624 {010, 001}, {011, 000}, {100, 001}, {100, 010}, %e A027624 {100, 011}, {101, 000}, {101, 010}, {101, 011}, %e A027624 {110, 000}, {110, 001}, {110, 011}, {110, 101}, %e A027624 {111, 000}, {111, 001}, {111, 010}, {111, 100}; %e A027624 the 8 triples whose subset pairs are all among the above 16 pairs: %e A027624 {100, 010, 001}, {101, 011, 000}, {110, 011, 000}, {110{ 111, 100,010 };εE A027 624,其子集三元组都在上述8个三元组中:{% %E A027 624 { 10, 01 }和{ } } } }和π=E,A027 624{{,π} },和{%}e E 017624{{}} } } } } } }。,101, 000 },εE A027 624 { 110, 101,011 },{ 111, 010,001 },{ 111, 100,001 },(2)四元组表示QY3的顶点2-着色。- _Daniel Forgues_, Feb 17 2015 %e A027624 a(4) = 743 since Q_4 is (...) with vertex adjacency submatrix M_4 = %e A027624 M_3 %e A027624 I_8 M_3 %e A027624 for 0 <= i <= 15 and 0 <= j < i (...) yielding the 1 + 16 trivial: (...); %e A027624 the 88 (= 16 + (64 - 8) + 16) pairs with adjacency 0: (...); %e A027624 the 208 triples: (...); the 228 quadruples: (...); %e A027624 the 128 quintuples: (...); the 56 sextuples: (...); %e A027624 the 16 (= 2 * (8 choose 7)) septuples: (...); %e A027624 and the 2 octuples (representing a vertex 2-coloring of Q_4): %e A027624 {110, 101, 011, 000} & 1 union {111, 100, 010, 001} & 0 = %e A027624 {1101, 1011, 0111, 0001, 1110, 1000, 0100, 0010} and %e A027624 {110, 101, 011, 000} & 0 union {111, 100, 010, 001} & 1 = %e A027624 {1100, 1010, 0110, 0000, 1111, 1001, 0101, 0011}. %e A027624 - _Daniel Forgues_, Feb 17-18 2015 %p A027624 Nbh:= proc(x) %p A027624 local i,n; %p A027624 n:= nops(x); %p A027624 {seq(subsop(i=1-x[i], x), i=1..n)}; %p A027624 end proc: %p A027624 F:= proc(S) option remember; %p A027624 local s, Sp; %p A027624 if nops(S) = 0 then return 1 fi; %p A027624 s:= S[1]; %p A027624 Sp:= S[2..-1]; %p A027624 F(Sp) + F(Sp minus Nbh(s)) %p A027624 end proc: %p A027624 G[0]:= {[]}: %p A027624 a[0]:= F(G[0]): %p A027624 for d from 1 to 6 do %p A027624 G[d]:= map(t -> ([0,op(t)],[1,op(t)]),G[d-1]); %p A027624 a[d]:= F(G[d]); %p A027624 od: %p A027624 seq(a[d],d=0..6); # _Robert Israel_, Feb 18 2015 %t A027624 stableSets[u_, Q_] := If[Length[u] === 0, {{}}, With[{w = First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w] & /@ stableSets[DeleteCases[u, r_ /; r === w || Q[r, w] || Q[w, r]], Q]]]]; %t A027624 Table[Length[stableSets[Subsets[Range[n]], And[Length[#1] + 1 === Length[#2], Complement[#1, #2] === {}] &]], {n, 0, 5}] (* _Gus Wiseman_, Mar 24 2016 *) %t A027624 Table[Length[Union @@ (Subsets /@ FindIndependentVertexSet[HypercubeGraph[n], Infinity, All])], {n, 0, 5}] (* _Eric W. Weisstein_, Sep 21 2017 *) %Y A027624 A000431(n+1),n>=1。(Qqn的独立顶点对).%%A027 624,NN,尼斯,更硬,更多的%AO A027 624 0,1%%A027 624.O.H.HurnNix%%E A027 624修正,A(0)由A.E.E.W.WeiStistin,JAN 04,2014,由.M.F.HasLeRyr重新建立,FEB 09 2015‰内容在OEIS最终用户许可协议下可用:HTTP:/OEIS.Org/Lub