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A star tree is a tree which consists of a single internal vertex (and n – 1 leaves). In other words, a star tree of order n is a tree of order n with as many leaves as possible. A caterpillar tree is a tree in which all vertices are within distance 1 of a central path subgraph.
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.
Some definitions allow a tree to have no nodes at all, in which case it is called empty. An internal node (also known as an inner node, inode for short, or branch node) is any node of a tree that has child nodes. Similarly, an external node (also known as an outer node, leaf node, or terminal node) is any node that does not have child nodes.
The data associated with a leaf cell varies by application, but the leaf cell represents a "unit of interesting spatial information". The subdivided regions may be square or rectangular, or may have arbitrary shapes. This data structure was named a quadtree by Raphael Finkel and J.L. Bentley in 1974. [1] A similar partitioning is also known as ...
As a result, = + also holds for a full binary tree. To make a binary tree with a leaf node without its sibling, a single leaf node is removed from a full binary tree, then "one leaf node removed" and "one internal nodes with two children removed" so = + also holds. This relation now covers all non-empty binary trees.
Tree: The full input Newick Format for a single tree Subtree: an internal node (and its descendants) or a leaf node Leaf: a node with no descendants Internal: a node and its one or more descendants BranchSet: a set of one or more Branches Branch: a tree edge and its descendant subtree.
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 ...
Figure 2 shows the conceptually same red–black tree without these NIL leaves. To arrive at the same notion of a path, one must notice that e.g., 3 paths run through the node 1, namely a path through 1 left plus 2 added paths through 1 right, namely the paths through 6 left and 6 right. This way, these ends of the paths are also docking points ...