Search results
Results from the WOW.Com Content Network
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.
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);
Proof without words that a hypercube graph is non-planar using Kuratowski's or Wagner's theorems and finding either K5 (top) or K3,3 (bottom) subgraphs. Kuratowski's research mainly focused on abstract topological and metric structures. He implemented the closure axioms (known in mathematical circles as the Kuratowski closure axioms). This was ...
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.
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.
A multidigraph is a directed graph which is permitted to have multiple arcs, i.e., arcs with the same source and target nodes. A multidigraph G is an ordered pair G := (V, A) with V a set of vertices or nodes, A a multiset of ordered pairs of vertices called directed edges, arcs or arrows.
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).