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A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column chart and has been identified as the prototype of charts. [1]
The graph-theoretic solution to the grid bracing problem has been generalized to double bracing, in which the grid should remain rigid even if one cross-brace fails, and to tension bracing, in which the diagonals of a grid are braced by wires and strings that can crumple to a shorter length but cannot be stretched to be longer.
Since these are technically letters, they have their own Unicode code points in the Latin Extended-B range: U+01C0 for the single bar and U+01C1 for the double bar. Some Northwest and Northeast Caucasian languages written in the Cyrillic script have a vertical bar called palochka (Russian: палочка , lit. 'little stick'), indicating the ...
Two red graphs are duals for the blue one, but they are not isomorphic. Because the dual graph depends on a particular embedding, the dual graph of a planar graph is not unique, in the sense that the same planar graph can have non-isomorphic dual graphs. [11] In the picture, the blue graphs are isomorphic but their dual red graphs are not.
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A skew-symmetric graph may equivalently be defined as the double covering graph of a polar graph or switch graph, [1] which is an undirected graph in which the edges incident to each vertex are partitioned into two subsets. Each vertex of the polar graph corresponds to two vertices of the skew-symmetric graph, and each edge of the polar graph ...
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Because no bin is allowed to be empty, there is at most one bar between any pair of stars. There are n − 1 gaps between stars and hence n − 1 positions in which a bar may be placed. A configuration is obtained by choosing k − 1 of these gaps to contain a bar; therefore there are () configurations.