login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A327362 Number of labeled connected graphs covering n vertices with at least one endpoint (vertex of degree 1). 6
0, 0, 1, 3, 28, 475, 14646, 813813, 82060392, 15251272983, 5312295240010, 3519126783483377, 4487168285715524124, 11116496280631563128723, 53887232400918561791887118, 513757147287101157620965656285, 9668878162669182924093580075565776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A graph is covering if the vertex set is the union of the edge set, so there are no isolated vertices.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..50

Gus Wiseman, The a(4) = 28 connected covering graphs with at least one endpoint.

FORMULA

Inverse binomial transform of A327364.

a(n) = A001187(n) - A059166(n). - Andrew Howroyd, Sep 11 2019

MATHEMATICA

csm[s_]:=With[{c=Select[Subsets[Range[Length[s]], {2}], Length[Intersection@@s[[#]]]>0&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];

Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n]&&Length[csm[#]]==1&&Min@@Length/@Split[Sort[Join@@#]]==1&]], {n, 0, 5}]

PROG

(PARI) seq(n)={Vec(serlaplace(-x^2/2 + log(sum(k=0, n, 2^binomial(k, 2)*x^k/k! + O(x*x^n))) - log(sum(k=0, n, 2^binomial(k, 2)*(x*exp(-x + O(x^n)))^k/k!))), -(n+1))} \\ Andrew Howroyd, Sep 11 2019

CROSSREFS

The non-connected version is A327227.

The non-covering version is A327364.

Graphs with endpoints are A245797.

Connected covering graphs are A001187.

Connected graphs with bridges are A327071.

Cf. A004110, A059166, A006125, A006129, A059166, A100743, A141580, A322395, A327105, A327229, A327230, A327366, A327369, A327377.

Sequence in context: A210854 A108288 A060545 * A327071 A058804 A327114

Adjacent sequences:  A327359 A327360 A327361 * A327363 A327364 A327365

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 04 2019

EXTENSIONS

Terms a(7) and beyond from Andrew Howroyd, Sep 11 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 11 16:42 EDT 2021. Contains 342888 sequences. (Running on oeis4.)