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A322396 Number of unlabeled simple connected graphs with n vertices whose bridges are all leaves, meaning at least one end of any bridge is an endpoint of the graph. 5
1, 1, 1, 2, 5, 18, 98, 779, 10589, 255790, 11633297, 1004417286, 163944008107, 50324877640599, 29001521193534445, 31396727025729968365, 63969154112074956299242, 245871360738448777028919520, 1787330701747389106609369225312, 24636017249593067184544456944967278 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..25

Eric Weisstein's World of Mathematics, Graph Bridge

Eric Weisstein's World of Mathematics, Endpoint

Gus Wiseman, The a(5) = 18 simple connected graphs whose bridges are all leaves.

PROG

(PARI) \\ See A004115 for graphsSeries and A339645 for combinatorial species functions.

bridgelessGraphs(n)={my(gc=sLog(graphsSeries(n)), gcr=sPoint(gc)); sSolve( gc + gcr^2/2 - sRaise(gcr, 2)/2, x*sv(1)*sExp(gcr) )}

cycleIndexSeries(n)={1+sSubstOp(bridgelessGraphs(n), symGroupSeries(n))}

NumUnlabeledObjsSeq(cycleIndexSeries(15)) \\ Andrew Howroyd, Dec 31 2020

CROSSREFS

Cf. A001187, A006125, A007146, A013922, A054921, A095983, A322338, A322394, A322395.

Sequence in context: A187008 A333837 A075634 * A007127 A279207 A005639

Adjacent sequences:  A322393 A322394 A322395 * A322397 A322398 A322399

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 06 2018

EXTENSIONS

a(6)-a(10) from Andrew Howroyd, Dec 08 2018

Terms a(11) and beyond from Andrew Howroyd, Dec 31 2020

STATUS

approved

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Last modified May 18 10:19 EDT 2021. Contains 343995 sequences. (Running on oeis4.)