Search results
Results From The WOW.Com Content Network
GrGen.NET, the graph rewrite generator, a graph transformation tool emitting C#-code or .NET-assemblies. GROOVE, a Java-based tool set for editing graphs and graph transformation rules, exploring the state spaces of graph grammars, and model checking those state spaces; can also be used as a graph transformation engine.
ΔY- and YΔ-transformations are a tool both in pure graph theory as well as applications. Both operations preserve a number of natural topological properties of graphs. . For example, applying a YΔ-transformation to a 3-vertex of a planar graph, or a ΔY-transformation to a triangular face of a planar graph, results again in a planar graph.
The transformation of graphs is often formalized and represented by graph rewrite systems. Complementary to graph transformation systems focusing on rule-based in-memory manipulation of graphs are graph databases geared towards transaction-safe, persistent storing and querying of graph-structured data.
A DPO graph transformation system (or graph grammar) consists of a finite graph, which is the starting state, and a finite or countable set of labeled spans in the category of finite graphs and graph homomorphisms, which serve as derivation rules. The rule spans are generally taken to be composed of monomorphisms, but the details can vary. [3]
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function, which is defined by the formula: [1] = + = + = ().
Compared to the graph y = f(x), the graph y = f(x − a) has been translated horizontally by a, while the graph y = f(x) + b has been translated vertically by b. The graph of a real function f , the set of points ( x , f ( x ) ) {\displaystyle (x,f(x))} , is often pictured in the real coordinate plane with x as the horizontal coordinate ...
Note: solving for ′ returns the resultant angle in the first quadrant (< <). To find , one must refer to the original Cartesian coordinate, determine the quadrant in which lies (for example, (3,−3) [Cartesian] lies in QIV), then use the following to solve for :
In particular, the Grötzsch graph and the Chvátal graph are triangle-free graphs requiring four colors, and the Mycielskian is a transformation of graphs that can be used to construct triangle-free graphs that require arbitrarily high numbers of colors.