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In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees.
This traversal is guided by the comparison function. In this case, the node always replaces a NULL reference (left or right) of an external node in the tree i.e., the node is either made a left-child or a right-child of the external node. After this insertion, if a tree becomes unbalanced, only ancestors of the newly inserted node are unbalanced.
A tree structure, tree diagram, or tree model is a way of representing the hierarchical nature of a structure in a graphical form. It is named a "tree structure" because the classic representation resembles a tree, although the chart is generally upside down compared to a biological tree, with the "stem" at the top and the "leaves" at the bottom.
2. A k-tree is a graph formed by gluing (k + 1)-cliques together on shared k-cliques. A tree in the ordinary sense is a 1-tree according to this definition. tree decomposition A tree decomposition of a graph G is a tree whose nodes are labeled with sets of vertices of G; these sets are called bags.
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 partially ordered set. However, if T is a tree of height > ω, then the Hasse diagram definition does not work.
In particular, the term "graph" was introduced by Sylvester in a paper published in 1878 in Nature, where he draws an analogy between "quantic invariants" and "co-variants" of algebra and molecular diagrams: [25] "[…] Every invariant and co-variant thus becomes expressible by a graph precisely identical with a Kekuléan diagram or
Tree topology, a topology based on a hierarchy of nodes in a computer network; Tree diagram (physics), an acyclic Feynman diagram, pictorial representations of the mathematical expressions governing the behavior of subatomic particles; Outliners, a common software application that is used to generate tree diagrams; Network diagram; Tree ...
A full binary tree (sometimes referred to as a proper, [15] plane, or strict binary tree) [16] [17] is a tree in which every node has either 0 or 2 children. Another way of defining a full binary tree is a recursive definition. A full binary tree is either: [11] A single vertex (a single node as the root node).