M-ary treeIn graph theory, an m-ary tree (for nonnegative integers m) (also known as n-ary, k-ary, k-way or generic tree) is an arborescence (or, for some authors, an ordered tree) in which each node has no more than m children. A binary tree is an important case where m = 2; similarly, a ternary tree is one where m = 3.
Tree (abstract data type)In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the root node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy).
Recursive definitionIn mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff). Some examples of recursively definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set. A recursive definition of a function defines values of the function for some inputs in terms of the values of the same function for other (usually smaller) inputs.
Empty setIn mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called non-empty.
Singleton (mathematics)In mathematics, a singleton (also known as a unit set or one-point set) is a set with exactly oneelement. For example, the set {0}{\displaystyle \{0\}} is a singleton whose single element is 0{\displaystyle 0}. PropertiesWithin the framework of Zermelo–Fraenkel set theory, the axiom of regularity guarantees that no set is an element of itself.
Graph theoryArea of discrete mathematicsA graph with 6 vertices and 7 edgesIn mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links, or lines).
Arborescence (graph theory)In graph theory, an arborescence is a directed graph where there exists a vertex r (called the root) such that, for any other vertex v, there is exactly one directed walk from r to v (noting that the root r is unique). An arborescence is thus the directed-graph form of a rooted tree, understood here as an undirected graph. An arborescence is also a directed rooted tree in which all edges point away from the root; a number of other equivalent characterizations exist.
Computer scienceStudy of computationFundamental areas of computer scienceProgramming language theoryComputer architectureArtificial intelligenceComputational complexity theoryComputer science is the study of computation, information, and automation, together with their associated phenomena.
Set theorySet theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.
TupleIn mathematics, a tuple is a finite sequence (or ordered list) of numbers. More generally, it is a sequence of mathematical objects, called the elements of the tuple. An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally used for "infinite sequences".
Graph (discrete mathematics)In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line).*As an Amazon Associate I earn from qualifying purchases.