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The name line graph comes from a paper by Harary & Norman (1960) although both Whitney (1932) and Krausz (1943) used the construction before this. [1] Other terms used for the line graph include the covering graph, the derivative, the edge-to-vertex dual, the conjugate, the representative graph, and the θ-obrazom, [1] as well as the edge graph ...
Line chart showing the population of the town of Pushkin, Saint Petersburg from 1800 to 2010, measured at various intervals. A line chart or line graph, also known as curve chart, [1] is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments. [2]
In graph theory, a line perfect graph is a graph whose line graph is a perfect graph. Equivalently, these are the graphs in which every odd-length simple cycle is a triangle. [1] A graph is line perfect if and only if each of its biconnected components is a bipartite graph, the complete graph K 4, or a triangular book K 1,1,n. [2]
The Grötzsch graph is an example of a 4-chromatic graph without a triangle, and the example can be generalized to the Mycielskians. Theorem ( William T. Tutte 1947 , [ 10 ] Alexander Zykov 1949 , Jan Mycielski 1955 ): There exist triangle-free graphs with arbitrarily high chromatic number.
This graph draws one or more independent numeric data series as lines. The data must be stored on Commons' Data namespace or come from Wikidata Query Service. Template parameters Parameter Description Type Status Table type tabletype Specifies the type of the table data. "tab" (default) uses data namespace on commons, without the data: prefix. "query" sends request to wikidata query service ...
Examples include the rook's graphs, the line graphs of complete bipartite graphs. Every line graph of a bipartite graph is an induced subgraph of a rook's graph. [20] Because line graphs of bipartite graphs are perfect, their clique number equals their chromatic number. The clique number of the line graph of a bipartite graph is the maximum ...
quasi-line graph A quasi-line graph or locally co-bipartite graph is a graph in which the open neighborhood of every vertex can be partitioned into two cliques. These graphs are always claw-free and they include as a special case the line graphs. They are used in the structure theory of claw-free graphs. quasi-random graph sequence
The Graph Literacy Scale [3] consists of 13 items and measures three abilities related to graph comprehension (see [11]) (1) the ability to read the data, that is, to find specific information in the graph; (2) the ability to read between the data, that is, to find relationships in the data as shown on the graph; and (3) the ability to read beyond the data, or make inferences and predictions ...