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A graph with intersection number four. The four shaded regions indicate cliques that cover all the edges of the graph. An alternative definition of the intersection number of a graph is that it is the smallest number of cliques in (complete subgraphs of ) that together cover all of the edges of .
The intersection number arises in the study of fixed points, which can be cleverly defined as intersections of function graphs with a diagonals. Calculating the intersection numbers at the fixed points counts the fixed points with multiplicity , and leads to the Lefschetz fixed-point theorem in quantitative form.
An UpSet Plot showing how movie genres intersect. The largest intersection of two sets is the Comedy-Drama intersection. UpSet plots are a data visualization method for showing set data with more than three intersecting sets. UpSet shows intersections in a matrix, with the rows of the matrix corresponding to the sets, and the columns to the ...
The line graph of a graph G is defined as the intersection graph of the edges of G, where we represent each edge as the set of its two endpoints. A string graph is the intersection graph of curves on a plane. A graph has boxicity k if it is the intersection graph of multidimensional boxes of dimension k, but not of any smaller dimension.
A collection of unit circles and the corresponding unit disk graph. In geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one vertex for each disk in the family, and with an edge between two vertices whenever the corresponding vertices lie within a ...
There are two steps when graphing the data which are to neglect all the points around zero on the y-axis to initially plot the line of best fit to find γ c ; however, when graphing the line initially if a point near 0 lands to the right of the intersection redo the regression including that point to make the measurement of the critical surface ...
To do this, we draw a line from the point of 50% on the axis of percentage until it intersects with the curve. Then we vertically project the intersection onto the horizontal axis. The last intersection gives us the desired value. The frequency polygon and ogive are used to compare two statistical sets whose number could be different.
In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and the distance between v and w. Some authors exclude the complete graphs and disconnected graphs from this definition.
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