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A327075 Number of non-connected unlabeled simple graphs covering n vertices. 12

%I #7 Sep 01 2019 08:39:32

%S 1,0,0,0,1,2,10,35,185,1242,13929,292131,12344252,1032326141,

%T 166163019475,50671385831320,29105332577409883,31455744378606296280,

%U 64032559078724993894492,245999991257359808853560276

%N Number of non-connected unlabeled simple graphs covering n vertices.

%C We consider the empty graph to be neither connected (one component) nor disconnected (more than one component).

%H Gus Wiseman, <a href="/A327075/a327075.png">The a(4) = 1 through a(6) = 10 non-connected covering graphs.</a>

%F a(n) = A002494(n) - A001349(n), if we assume A001349(0) = A001349(1) = 0.

%e Non-isomorphic representatives of the a(0) = 1 through a(6) = 10 graphs (empty columns not shown):

%e {} {12,34} {12,35,45} {12,34,56}

%e {12,34,35,45} {12,35,46,56}

%e {12,36,46,56}

%e {13,23,46,56}

%e {12,34,35,46,56}

%e {12,36,45,46,56}

%e {13,23,45,46,56}

%e {12,13,23,45,46,56}

%e {12,35,36,45,46,56}

%e {12,34,35,36,45,46,56}

%Y Column k = 0 of A327201.

%Y The labeled version is A327070.

%Y Disconnected graphs are A000719.

%Y Cf. A000088, A001187, A001349, A002494, A006129, A054592.

%K nonn

%O 0,6

%A _Gus Wiseman_, Aug 26 2019

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