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http://dx.doi.org/10.5831/HMJ.2017.39.4.493

THE NUMBER OF (d, k)-HYPERTREES

Chae, Gab-Byung (Division of Mathematics and Informational Statistics, Wonkwang University)
Siu, Wai-Cheong (School of Business, Macao Polytechnic Institute)

Publication Information

Honam Mathematical Journal / v.39, no.4, 2017 , pp. 493-501 More about this Journal

Abstract

In this paper, we define and enumerate two tree-like hypergraph structures which we call them (d, k)-trees and d-trees, where $d{\geq}2$ and k > 0 are integers. These new definitions generalize traditional and HP-hypertrees.

Keywords

Enumeration; hypertrees;

Citations & Related Records

Reference

1	C. Berge, Graphs et Hypergraphes, Dunod, 1970.
2	C. Berge, Introduction A La Theorie Des Hypergraphes, Les Presses De L'Universite De Montreal, 1973.
3	C. Berge, Hypergraphs, North-Holland, 1989.
4	L.W. Beineke and J.W. Moon, Several Proofs of the Number of labelled 2-Dimensional Trees, Proof Techniques in Graph Theory, Academic New York, 1969.
5	L.W. Beineke and R.E. Pippert, Characterizations of 2-Dimensional Trees(to appear).
6	L.W. Beineke and R.E. Pippert, The number of labelled k-dimensional trees, Journal of Combinatorial Theory 6 (1969), 200-205. DOI
7	A. Cayley, A Theorem on Trees, Quart. J. Math. 23, (1889), 376-378, Collected Pares, Cambridge, 13, (1897), 26-28.
8	K. Husimi, Note on Mayer's Theory of Cluster Integrals, J. Chem. Phys. 18, (1950), 682-684. DOI
9	J. W. Moon, Various Proofs of Cayley's Formula for Counting Trees, in A Sem-inar in Graph Theory (F. Harary, ed.), NewYork, (1967), 70-78
10	J. W. Moon, Counting Labelled Trees, Canadian Mathematical Monographs, 1970.
11	F. Harary and E. M. Palmer, On acyclic simplicial complexes, Mathematika 15, (1968), 115-122. DOI