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A clique-sum of two planar graphs and the Wagner graph, forming a K 5-free graph. In graph theory , Wagner's theorem is a mathematical forbidden graph characterization of planar graphs , named after Klaus Wagner , stating that a finite graph is planar if and only if its minors include neither K 5 (the complete graph on five vertices ) nor K 3,3 ...
Characterise word-representable near-triangulations containing the complete graph K 4 (such a characterisation is known for K 4-free planar graphs [17]). Classify graphs with representation number 3. (See [30] for the state-of-the-art in this direction.) Is the line graph of a non-word-representable graph always non-word-representable?
You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses ...
The R programming language can be used for creating Wikipedia graphs. The Google Chart API allows a variety of graphs to be created. Livegap Charts creates line, bar, spider, polar-area and pie charts, and can export them as images without needing to download any tools. Veusz is a free scientific graphing tool that can produce 2D and 3D plots ...
A term graph is a representation of an expression in a formal language as a generalized graph whose vertices are terms [clarify]. [1] Term graphs are a more powerful form of representation than expression trees because they can represent not only common subexpressions (i.e. they can take the structure of a directed acyclic graph) but also cyclic/recursive subexpressions (cyclic digraphs).
At a meeting with financial analysts in July 2000, Microsoft demonstrated Office XP, then known by its codename, Office 10, which included a subset of features Microsoft designed in accordance with what at the time was known as the .NET strategy, one by which it intended to provide extensive client access to various web services and features such as speech recognition. [17]
Use the editor menu to change your font, font color, add hyperlinks, images and more. 1. Launch AOL Desktop Gold. 2. Sign on with your username and password.
A bar graph shows comparisons among discrete categories. One axis of the chart shows the specific categories being compared, and the other axis represents a measured value. Some bar graphs present bars clustered in groups of more than one, showing the values of more than one measured variable. These clustered groups can be differentiated using ...