# ON NUMBER OF WAYS TO SHELL THE k-DIMENSIONAL TREES

• Published : 2007.05.31
• 54 5

#### Abstract

Which spheres are shellable?[2]. We present one of them which is the k-tree with n-labeled vertices. We found that the number of ways to shell the k-dimensional trees on n-labeled vertices is $$\frac{n!}{(k+1)!}(nk-k^2-k+1)!k$$.

#### Keywords

k-tree;recursive k-tree;shell

#### References

1. L. W. Beineke and R. E. Pippert, The number of labeled k-dimensional trees, J. Combinatorial Theory 6 (1969), 200-205 https://doi.org/10.1016/S0021-9800(69)80120-1
2. F. Harary, The number of linear, directed, rooted, and connected graphs, Trans. Amer. Math. Soc. 78 (1955), 445-463 https://doi.org/10.2307/1993073
3. F. Harary and E. M. Palmer, On acyclic simplicial complexes, Mathematika 15 (1968), 115-122 https://doi.org/10.1112/S002557930000245X
4. E. M. Palmer, On the number of labeled 2-trees, J. Combinatorial Theory 6 (1969), 206-207 https://doi.org/10.1016/S0021-9800(69)80121-3
5. N. J. A. Sloane and S. Plouffe, The encyclopedia of integer sequences, With a separately available computer disk. Academic Press, Inc., San Diego, CA, 1995
6. G. Danaraj and V. Klee, Which spheres are shellable?, Ann. Discrete Math. 2 (1978), 33-52 https://doi.org/10.1016/S0167-5060(08)70320-0