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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.
Trees with a single root may be viewed as rooted trees in the sense of graph theory in one of two ways: either as a tree (graph theory) or as a trivially perfect graph. 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 ...
Pages in category "Fields of mathematics" The following 5 pages are in this category, out of 5 total. This list may not reflect recent changes. *
Mathematics is a broad subject that is commonly divided in many areas or branches that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers .
The branch of mathematics deals with the properties and relationships of numbers, especially positive integers. Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory ...
Every tree in descriptive set theory is also an order-theoretic tree, using a partial ordering in which two sequences and are ordered by < if and only if is a proper prefix of . The empty sequence is the unique minimal element, and each element has a finite and well-ordered set of predecessors (the set of all of its prefixes).
In 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 ).
Communication technologies apply branches of mathematics that may be very old (e.g., arithmetic), especially with respect to transmission security, in cryptography and coding theory. Discrete mathematics is useful in many areas of computer science, such as complexity theory , information theory , and graph theory . [ 138 ]