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A tree whose root node has two subtrees, both of which are full binary trees. A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level (the level of a node defined as the number of edges or links from the root node to a node). [18] A perfect binary tree is a full ...
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.
Since this is a complete graph, every two nodes in A must be friends and every two nodes in B must be friends, otherwise there would be a 3-cycle which was unbalanced. (Since this is a complete graph, any one negative edge would cause an unbalanced 3-cycle.) Likewise, all negative edges must go between the two groups. [6]
Henzinger and King [2] suggest to represent a given tree by keeping its Euler tour in a balanced binary search tree, keyed by the index in the tour. So for example, the unbalanced tree in the example above, having 7 nodes, will be represented by a balanced binary tree with 14 nodes, one for each time each node appears on the tour.
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.
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 free tree or unrooted tree is a connected undirected graph with no cycles. The vertices with one neighbor are the leaves of the tree, and the remaining vertices are the internal nodes of the tree. The degree of a vertex is its number of neighbors; in a tree with more than one node, the leaves are the vertices of degree one. An unrooted binary ...