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  2. Kruskal's tree theorem - Wikipedia

    en.wikipedia.org/wiki/Kruskal's_tree_theorem

    A sequence of rooted trees labelled from a set of 3 labels (blue < red < green). The n th tree in the sequence contains at most n vertices, and no tree is inf-embeddable within any later tree in the sequence. TREE(3) is defined to be the longest possible length of such a sequence.

  3. Cayley's formula - Wikipedia

    en.wikipedia.org/wiki/Cayley's_formula

    Each labelled rooted forest can be turned into a labelled tree with one extra vertex, by adding a vertex with label n + 1 and connecting it to all roots of the trees in the forest. There is a close connection with rooted forests and parking functions , since the number of parking functions on n cars is also ( n + 1) n − 1 .

  4. Tree (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Tree_(graph_theory)

    A rooted tree T that is a subgraph of some graph G is a normal tree if the ends of every T-path in G are comparable in this tree-order (Diestel 2005, p. 15). Rooted trees, often with an additional structure such as an ordering of the neighbors at each vertex, are a key data structure in computer science; see tree data structure.

  5. Arborescence (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Arborescence_(graph_theory)

    The term arborescence comes from French. [6] Some authors object to it on grounds that it is cumbersome to spell. [7] There is a large number of synonyms for arborescence in graph theory, including directed rooted tree, [3] [7] out-arborescence, [8] out-tree, [9] and even branching being used to denote the same concept. [9]

  6. Tree (set theory) - Wikipedia

    en.wikipedia.org/wiki/Tree_(set_theory)

    Trees with a single root may be viewed as rooted trees in the sense of graph theory in one of two ways: either as a tree (graph theory) or as a trivially perfect graph. In the first case, the graph is the undirected Hasse diagram of the partially ordered set, and in the second case, the graph is simply the underlying (undirected) graph of the ...

  7. Rooted graph - Wikipedia

    en.wikipedia.org/wiki/Rooted_graph

    A special case of interest are rooted trees, the trees with a distinguished root vertex. If the directed paths from the root in the rooted digraph are additionally restricted to be unique, then the notion obtained is that of (rooted) arborescence—the directed-graph equivalent of a rooted tree. [7]

  8. List of phylogenetic tree visualization software - Wikipedia

    en.wikipedia.org/wiki/List_of_phylogenetic_tree...

    an online tool for phylogenetic tree view (newick format) that allows multiple sequence alignments to be shown together with the trees (fasta format) EvolView [3] an online tool for visualizing, annotating and managing phylogenetic trees IcyTree [4] Client-side Javascript SVG viewer for annotated rooted trees. Also supports phylogenetic networks

  9. m-ary tree - Wikipedia

    en.wikipedia.org/wiki/M-ary_tree

    The left chain of T is a sequence of ,, …, nodes such that is the root and all nodes except have one child connected to their left most (i.e., []) pointer. Any m- ary tree can be transformed to a left-chain tree using sequence of finite left-t rotations for t from 2 to m .

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