Search results
Results from the WOW.Com Content Network
In the mathematics of graph drawing, the crossing number inequality or crossing lemma gives a lower bound on the minimum number of edge crossings in a plane drawing of a given graph, as a function of the number of edges and vertices of the graph.
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. [1] [2] Such a drawing is called a plane graph, or a planar embedding of the graph.
A drawing of the Heawood graph with three crossings. This is the minimum number of crossings among all drawings of this graph, so the graph has crossing number cr(G) = 3.. In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G.
For example, [3] to draw the solution set of x + 3y < 9, one first draws the line with equation x + 3y = 9 as a dotted line, to indicate that the line is not included in the solution set since the inequality is strict. Then, pick a convenient point not on the line, such as (0,0).
The formula was defined by Jeff Tupper and appears as an example in Tupper's 2001 SIGGRAPH paper on reliable two-dimensional computer graphing algorithms. [1] This paper discusses methods related to the GrafEq formula-graphing program developed by Tupper. [2] Although the formula is called "self-referential", Tupper did not name it as such. [3]
Crossing Numbers of Graphs is a book in mathematics, on the minimum number of edge crossings needed in graph drawings. It was written by Marcus Schaefer, a professor of computer science at DePaul University , and published in 2018 by the CRC Press in their book series Discrete Mathematics and its Applications.
See also Category:Geometric graph theory and Category:Topological graph theory. This category is about Graph (discrete mathematics)s, as defined in discrete mathematics, and not about graph of a function.
The curve is a graph showing the proportion of overall income or wealth assumed by the bottom x% of the people, although this is not rigorously true for a finite population (see below). It is often used to represent income distribution , where it shows for the bottom x % of households, what percentage ( y %) of the total income they have.