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A004110 Number of n-node unlabeled graphs without endpoints (i.e., no nodes of degree 1).
(Formerly M1504)
1, 1, 1, 2, 5, 16, 78, 588, 8047, 205914, 10014882, 912908876, 154636289460, 48597794716736, 28412296651708628, 31024938435794151088, 63533059372622888758054, 244916078509480823407040988, 1783406527599529094009748567708 (list; graph; refs; listen; history; text; internal format)



a(n) is also the number of unlabeled mating graphs with n nodes. A mating graph has no two vertices with identical sets of neighbors. [Tanya Khovanova, Oct 23 2008]


F. Harary, Graph Theory, Wiley, 1969. See illustrations in Appendix 1.

F. Harary and E. Palmer, Graphical Enumeration, (1973), compare formula (8.7.11).

R. W. Robinson, personal communication.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.

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


R. W. Robinson, Table of n, a(n) for n = 0..26

David Cook II, Nested colourings of graphs, arXiv preprint arXiv:1306.0140 [math.CO], 2013

Ji Li, Ji Li's Research page [From Tanya Khovanova, Oct 23 2008]

R. J. Mathar, Illustrations for n=1..5 nodes

R. W. Robinson, Graphs without endpoints - computer printout

N. J. A. Sloane, Illustration of a(0)-a(5)


Cf. A059166 (n-node connected labeled graphs without endpoints), A059167 (n-node labeled graphs without endpoints), A004108 (n-node connected unlabeled graphs without endpoints).

If isolated nodes are forbidden, see A261919.

Cf. A006024 (number of labeled mating graphs with n nodes). [Tanya Khovanova, Oct 23 2008]

Sequence in context: A263914 A218168 A054960 * A236960 A290609 A048754

Adjacent sequences:  A004107 A004108 A004109 * A004111 A004112 A004113




N. J. A. Sloane



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Last modified March 23 02:54 EDT 2018. Contains 301097 sequences. (Running on oeis4.)