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The induced graph of an ordered graph is obtained by adding some edges to an ordering graph, using the method outlined below. The induced width of an ordered graph is the width of its induced graph. [2] Given an ordered graph, its induced graph is another ordered graph obtained by joining some pairs of nodes that are both parents of another node.
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, [1] and divisor graphs. [2] An incomparability graph is an undirected graph that connects pairs of elements that are not comparable to each other in a partial order .
A directed graph is weakly connected (or just connected [9]) if the undirected underlying graph obtained by replacing all directed edges of the graph with undirected edges is a connected graph. A directed graph is strongly connected or strong if it contains a directed path from x to y (and from y to x) for every pair of vertices (x, y).
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
The ordered pair (a, b) is different from the ordered pair (b, a), unless a = b. In contrast, the unordered pair, denoted {a, b}, always equals the unordered pair {b, a}. Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a computer science context) of length 2. Ordered pairs of scalars are sometimes called 2-dimensional ...
Since then, the interaction between mathematical innovations and scientific discoveries has led to a correlated increase in the development of both. [5] At the end of the 19th century, the foundational crisis of mathematics led to the systematization of the axiomatic method , [ 6 ] which heralded a dramatic increase in the number of ...
Probability density functions of the order statistics for a sample of size n = 5 from an exponential distribution with unit scale parameter In statistics , the k th order statistic of a statistical sample is equal to its k th-smallest value. [ 1 ]
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