Search results
Results From The WOW.Com Content Network
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.
In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest treewidth is 1; the graphs with treewidth 1 are exactly the trees and the forests. An example of graphs with treewidth at most 2 are the series–parallel graphs.
Paths through an arbitrary node-and-edge graph (including multigraphs), by making multiple nodes in the tree for each graph node used in multiple paths; Any mathematical hierarchy; Tree structures are often used for mapping the relationships between things, such as: Components and subcomponents which can be visualized in an exploded-view drawing
Each tree node lists at most three vertices, so the width of this decomposition is two. In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the graph. Tree decompositions are also called junction trees, clique trees ...
In graph theory, the tree-depth of a connected undirected graph is a numerical invariant of , the minimum height of a Trémaux tree for a supergraph of .This invariant and its close relatives have gone under many different names in the literature, including vertex ranking number, ordered chromatic number, and minimum elimination tree height; it is also closely related to the cycle rank of ...
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.
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 set theory, a tree is a partially ordered set (T, <) such that for each t ∈ T, the set {s ∈ T : s < t} is well-ordered by the relation <. Frequently trees are assumed to have only one root (i.e. minimal element ), as the typical questions investigated in this field are easily reduced to questions about single-rooted trees.