A327200 - OEIS

A327200

Number of labeled graphs with n vertices and non-spanning edge-connectivity >= 2.

0, 0, 0, 4, 42, 718, 26262, 1878422, 256204460, 67525498676, 34969833809892, 35954978661632864, 73737437034063350534, 302166248212488958298674, 2475711390267267917290354410, 40563960064630744031043287569378, 1329219366981359393514586291328267704

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

OFFSET

0,4

COMMENTS

The non-spanning edge-connectivity of a graph is the minimum number of edges that must be removed to obtain a graph whose edge-set is disconnected or empty.

LINKS

Table of n, a(n) for n=0..16.

Gus Wiseman, The a(4) = 42 graphs with non-spanning edge-connectivity >= 2.

FORMULA

Binomial transform of A322395, if we assume A322395(0) = A322395(1) = A322395(2) = 0.

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]]]]]]]]];

eConn[sys_]:=If[Length[csm[sys]]!=1, 0, Length[sys]-Max@@Length/@Select[Union[Subsets[sys]], Length[csm[#]]!=1&]];

Table[Length[Select[Subsets[Subsets[Range[n], {2}]], eConn[#]>=2&]], {n, 0, 5}]

CROSSREFS

Row sums of A327148 if the first two columns are removed.

BII-numbers of set-systems with non-spanning edge-connectivity >= 2 are A327102.

Graphs with non-spanning edge-connectivity 1 are A327231.

Cf. A001187, A006129, A095983, A182100, A322395, A326787, A327076, A327079, A327097, A327099, A327236.

Sequence in context: A136045 A192949 A156453 * A259062 A074768 A295763

Adjacent sequences: A327197 A327198 A327199 * A327201 A327202 A327203

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 01 2019

STATUS

approved