Years and Authors of Summarized Original Work
2002; Nakano
2004; Nakano, Uno
2012; Yamanaka, Otachi, Nakano
Problem Definition
A tree is a connected graph with no cycle. A rooted tree is a tree with one designated vertex, called the root. For each vertex v except the root in a rooted tree, the parent of v is the neighbor vertex of v on the path between v and the root. If vertex p is the parent of vertex c, then c is a child of p. An ordered tree is a rooted tree in which the children of each vertex are ordered. The five ordered trees having four vertices are shown in Fig. 1. An unordered tree is a rooted tree in which the ordering of the children of each vertex does not matter. The four ordered trees having four vertices are shown in Fig. 2
The ordered trees with four vertices
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Recommended Reading
Avis D, Fukuda K (1996) Reverse search for enumeration. Discret Appl Math 65(1–3):21–46
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Rosen KH(Ed) (1999) Handbook of discrete and combinatorial mathematics. CRC, Boca Raton
Yamanaka K, Otachi Y, Nakano S (2012) Efficient enumeration of ordered trees with k leaves. Theor Comput Sci 442:2–27
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Nakano, Si. (2016). Tree Enumeration. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_726
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