A003089 Number of connected line graphs with n nodes. (Formerly M1417)

1, 1, 2, 5, 12, 30, 79, 227, 710, 2322, 8071, 29503, 112822, 450141, 1867871, 8037472, 35787667, 164551477, 779945969, 3804967442, 19079312775, 98211456209, 518397621443, 2802993986619, 15510781288250, 87765472487659, 507395402140211, 2994893000122118, 18035546081743772, 110741792670074054, 692894304050453139

Offset

1,3

Comments

Sequence is identical to the number of connected graphs on n edges (A002905), except for the term a(3). The three connected 3-edge graphs (P_4, K_3 and K_{1,3}) yield only two linegraphs because K_3 and K_{1,3} have isomorphic linegraphs. No other connected nonisomorphic graphs have isomorphic linegraphs.

References

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 221.

R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Max Alekseyev, Table of n, a(n) for n = 1..60

Eric Weisstein's World of Mathematics, Line Graph.

Crossrefs

Cf. A002905.

Sequence in context: A120895 A101785 A363306 * A213263 A179544 A182488

Adjacent sequences: A003086 A003087 A003088 * A003090 A003091 A003092

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from Ronald C. Read.

More terms from Gordon F. Royle, Jun 05 2003

a(25)-a(26) from Max Alekseyev, Nov 25 2013

a(27) and beyond from Max Alekseyev, Sep 07 2016

Status

approved