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For example, on the natural numbers, < is connected, while "is a divisor of " is not (e.g. neither 5R7 nor 7R5). Strongly connected for all x, y ∈ X, xRy or yRx. For example, on the natural numbers, ≤ is strongly connected, but < is not. A relation is strongly connected if, and only if, it is connected and reflexive.
The ordered pair (a, b) is different from the ordered pair (b, a), unless a = b. In contrast, the unordered pair, denoted {a, b}, 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 vectors.
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.
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.
A directed graph or digraph is a graph in which edges have orientations. In one restricted but very common sense of the term, [5] a directed graph is an ordered pair = (,) comprising: , a set of vertices (also called nodes or points);
Illustration of a plane, showing the absolute values (unsigned dotted line lengths) of the coordinates of the points (2, 3), (0, 0), (−3, 1), and (−1.5, −2.5). The first of these signed ordered pairs is the abscissa of the corresponding point, and the second value is its ordinate.