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.

1, 1, 1, 2, 5, 18, 98, 779, 10589, 255790, 11633297, 1004417286, 163944008107, 50324877640599, 29001521193534445, 31396727025729968365, 63969154112074956299242, 245871360738448777028919520, 1787330701747389106609369225312, 24636017249593067184544456944967278

Offset: 0

Author

Gus Wiseman, Dec 06 2018

Keywords

• nonn

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.

Crossrefs

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

Programs

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

Extensions

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

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