0,6

A tree has either a center or a bicenter and either a centroid or a bicentroid. (These terms were introduced by Jordan.)

If the number of edges in a longest path in the tree is 2m, then the middle node in the path is the unique center, otherwise the two middle nodes in the path are the unique bicenters.

N. L. Biggs et al., Graph Theory 1736-1936, Oxford, 1976, p. 49.

A. Cayley, On the analytical forms called trees, with application to the theory of chemical combinations, Reports British Assoc. Advance. Sci. 45 (1875), 257-305 = Math. Papers, Vol. 9, 427-460 (see p. 438).

A. Cayley, On the analytical forms called trees, Amer. J. Math., 4 (1881), 266-268.

F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1994; pp. 35, 36.

C. Jordan, Sur les assemblages des lignes, J. Reine angew. Math., 70 (1869), 185-190.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

N. J. A. Sloane, Table of n, a(n) for n = 0..200

E. M. Rains and N. J. A. Sloane, On Cayley's Enumeration of Alkanes (or 4-Valent Trees), J. Integer Sequences, Vol. 2 (1999), Article 99.1.1. [This articles states incorrectly that A000676 and A000677 give the numbers of trees with respectively a centroid and bicentroid.]

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to trees

Cf. A102911 (trees with a bicentroid), A027416 (trees with a centroid), A000677 (trees with a bicenter), A000055 (trees), A000081 (rooted trees).

A000676+A000677 = A000055.

Sequence in context: A054272 A129016 A099163 this_sequence A032173 A130616 A089324

Adjacent sequences: A000673 A000674 A000675 this_sequence A000677 A000678 A000679

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).