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graph intersection: G 1 ∩ G 2 = (V 1 ∩ V 2, E 1 ∩ E 2); [1] graph join: . Graph with all the edges that connect the vertices of the first graph with the vertices of the second graph. It is a commutative operation (for unlabelled graphs); [2] graph products based on the cartesian product of the vertex sets:
In particular, every graph property expressible as a first-order sentence can be tested in linear time for the graphs of bounded expansion. These are the graphs in which all shallow minors are sparse graphs, with a ratio of edges to vertices bounded by a function of the depth of the minor. Even more generally, first-order model checking can be ...
A directed graph is called an oriented graph if none of its pairs of vertices is linked by two mutually symmetric edges. Among directed graphs, the oriented graphs are the ones that have no 2-cycles (that is at most one of (x, y) and (y, x) may be arrows of the graph). [1] A tournament is an orientation of a complete graph.
A line perfect graph. The edges in each biconnected component are colored black if the component is bipartite, blue if the component is a tetrahedron, and red if the component is a book of triangles. The line graph of the complete graph K n is also known as the triangular graph, the Johnson graph J(n, 2), or the complement of the Kneser graph ...
The graph of this function is shown to the right. Since the graph of an affine(*) function is a line , the graph of a piecewise linear function consists of line segments and rays . The x values (in the above example −3, 0, and 3) where the slope changes are typically called breakpoints, changepoints, threshold values or knots.
RAC drawings of the complete graph K 5 and the complete bipartite graph K 3,4. In graph drawing, a RAC drawing of a graph is a drawing in which the vertices are represented as points, the edges are represented as straight line segments or polylines, at most two edges cross at any point, and when two edges cross they do so at right angles to each other.
Image source: The Motley Fool. Confluent (NASDAQ: CFLT) Q4 2024 Earnings Call Feb 11, 2025, 4:30 p.m. ET. Contents: Prepared Remarks. Questions and Answers. Call ...
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).