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2. Tree (graph theory) - Wikipedia

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

   The root has depth zero, leaves have height zero, and a tree with only a single vertex (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (a tree with no vertices, if such are allowed) has depth and height −1. A k-ary tree (for nonnegative integers k) is a rooted tree in which each vertex has at most k children.

3. Tree (abstract data type) - Wikipedia

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

   The height of the root is the height of the tree. The depth of a node is the length of the path to its root (i.e., its root path). Thus the root node has depth zero, leaf nodes have height zero, and a tree with only a single node (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (tree with no nodes, if such ...

4. Longest path problem - Wikipedia

   en.wikipedia.org/wiki/Longest_path_problem

   Use the sequence of root-to-leaf paths of the depth-first search tree, in the order in which they were traversed by the search, to construct a path decomposition of the graph, with pathwidth . Apply dynamic programming to this path decomposition to find a longest path in time O ( d ! 2 d n ) {\displaystyle O(d!2^{d}n)} , where n {\displaystyle ...

5. Rooted graph - Wikipedia

   en.wikipedia.org/wiki/Rooted_graph

   In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. [1] [2] Both directed and undirected versions of rooted graphs have been studied, and there are also variant definitions that allow multiple roots. Examples of rooted graphs with some variants.

6. Ternary tree - Wikipedia

   en.wikipedia.org/wiki/Ternary_tree

   The root node is at depth zero. Height - Length of the path from the root to the deepest node in the tree. A (rooted) tree with only one node (the root) has a height of zero. In the example diagram, the tree has height of 2. Sibling - Nodes that share the same parent node. A node p is an ancestor of a node q if it exists on the path from q to ...

7. Game tree - Wikipedia

   en.wikipedia.org/wiki/Game_tree

   The complete game tree for a game is the game tree starting at the initial position and containing all possible moves from each position; the complete tree is the same tree as that obtained from the extensive-form game representation. To be more specific, the complete game is a norm for the game in game theory.