A066951 -id:A066951 - cp's OEIS frontend

A046091 Number of connected planar graphs with n edges.

1, 1, 1, 3, 5, 12, 30, 79, 227, 709, 2318, 8049, 29372, 112000, 444855, 1833072, 7806724, 34252145, 154342391, 712231465, 3357126655, 16119421175, 78580665333

Offset: 0

Brendan McKay

Inverse Euler transform of A343872. - Andrew Howroyd, May 05 2021

			a(3) = 3 since the three connected graphs with three edges are a path, a triangle and a "Y".
The first difference between this sequence and A002905 is for n=9 edges where we see K_{3,3}, the "utility graph".

B. D. McKay and A. Piperno, Practical Graph Isomorphism, II, J. Symbolic Computation, 60 (2014), pp. 94-112.
Eric Weisstein's World of Mathematics, Planar Connected Graph.

Row sums of A343873.
Column sums of A049334.
Cf. A002905, A003094, A066951, A291842, A343869, A343872.

# count graphs for the sequence by number of vertices v, sum over v afterwards
geng -c $v $n:$n | planarg -q | countg -q # Georg Grasegger, Jul 06 2023

a(11)-a(19) from Martin Fuller using nauty by Brendan McKay, Mar 07 2015

a(20)-a(22) added by Georg Grasegger, Jul 06 2023

A003055 Number of connected graphs, up to homeomorphism, that can be drawn in the plane using unit-length edges.

Original entry on oeis.org

1, 1, 3, 5, 10, 19, 39, 84, 196, 479

Offset: 1

N. J. A. Sloane

K_4 can't be so drawn even though it is planar. Although a square with a tail of length 1 and a triangle with a tail of length 2 are nonisomorphic graphs with five edges, they are homeomorphic as topological spaces.

M. Gardner, The Unexpected Hanging and Other Mathematical Diversions. Simon and Schuster, NY, 1969, p. 80.
R. C. Read, From Forests to Matches, Journal of Recreational Mathematics, Vol. 1:3 (Jul 1968), 60-172.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Jean-Paul Delahaye, Les graphes-allumettes, (in French), Pour la Science no. 445, November 2014.
Raffaele Salvia, A catalogue of matchstick graphs, arXiv:1303.5965 [math.CO], 2013-2015.
Alexis Vaisse, Matchstick graphs
Eric Weisstein's World of Mathematics, Match Problem
Wikipedia, Matchstick graph

Cf. A066951.

Corrected by Brendan McKay and Les Reid (les(AT)math.smsu.edu), May 25 2002
Reference and a(8) from Read's paper added by William Rex Marshall, Nov 16 2010
a(9) from Salvia's paper added by Brendan McKay, Apr 13 2013
a(9) corrected from version 5 [Jan 05 2015] of Salvia's paper; a(10) from Vaisse's webpage added by Raffaele Salvia, Jan 31 2015

A176425 Number of connected planar graphs with at most n edges.

Original entry on oeis.org

1, 2, 3, 6, 11, 23, 53, 132, 359, 1068, 3386, 11435, 40807, 152807, 597662, 2430734, 10237458, 44489603, 198831994, 911063459

Offset: 0

Jonathan Vos Post, Apr 17 2010

Partial sums of number of connected planar graphs with n edges (A046091).

Table of n, a(n) for n = 0..19

Cf. A002905, A066951, A046091.

a(n) = Sum_{i=0..n} A046091(i).

New name from Bartlomiej Pawlik, May 31 2022

cp's OEIS Frontend

A046091 Number of connected planar graphs with n edges.

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A003055 Number of connected graphs, up to homeomorphism, that can be drawn in the plane using unit-length edges.

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A176425 Number of connected planar graphs with at most n edges.

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