A004108 -id:A004108 - cp's OEIS frontend

A241905 The number of connected graphs G on n vertices such that every unlabeled automorphism of the reduced graph of G is a labeled automorphism of the reduced graph of G.

Original entry on oeis.org

1, 1, 1, 4, 13, 83

Offset: 1

Dayana Adatorwovor, May 01 2014

R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford University Press (1999).

J. P. McSorley and T. D. Porter, K_p Removable Sequences of Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, 45, 43-62, (2003).

Cf. A004110, A004108, A241904 (similar but graphs not necessarily connected).

A369284 Number of point-determining graphs on n unlabeled nodes with no isolated vertices.

Original entry on oeis.org

1, 0, 1, 1, 4, 12, 66, 522, 7525, 198389, 9816493, 903092383, 153733197077, 48444061519659, 28363852590188969, 30996574583203962119, 63502062798039684795935, 244852576446682783722245053, 1783161675023082411226026322655, 24603891461799405333437840036319801

Offset: 0

Andrew Howroyd, Jan 18 2024

nonn

Point-determining graphs are also called mating graphs. See A004110 for references.

The inverse Euler transform of this sequence gives A004108 except with a(1) = 0 and a(2) = 1.

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

Cf. A004108, A004110 (point-determining graphs).

a(n) = A004110(n) - a(n-1) for n > 0.

G.f.: B(x)/(1 + x) where B(x) is the g.f. of A004110.

A101390 Number of n-vertex unlabeled mating graphs (cf. A006024) without endpoints.

Original entry on oeis.org

1, 0, 1, 2, 7, 41, 347, 5447, 158097, 8456025

Offset: 1

Goran Kilibarda, Zoran Maksimovic, Vladeta Jovovic, Jan 14 2005

Cf. A006024, A004108, A004110, A059167.

cp's OEIS Frontend

A241905 The number of connected graphs G on n vertices such that every unlabeled automorphism of the reduced graph of G is a labeled automorphism of the reduced graph of G.

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A369284 Number of point-determining graphs on n unlabeled nodes with no isolated vertices.

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A101390 Number of n-vertex unlabeled mating graphs (cf. A006024) without endpoints.

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