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The automorphism group of the free group with ordered basis [ x 1, …, x n] is generated by the following 4 elementary Nielsen transformations: Switch x 1 and x 2; Cyclically permute x 1, x 2, …, x n, to x 2, …, x n, x 1. Replace x 1 with x 1 −1; Replace x 1 with x 1 ·x 2; These transformations are the analogues of the elementary row ...
Sometimes graph grammar is used as a synonym for graph rewriting system, especially in the context of formal languages; the different wording is used to emphasize the goal of constructions, like the enumeration of all graphs from some starting graph, i.e. the generation of a graph language – instead of simply transforming a given state (host ...
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.
In mathematics, especially in the area of modern algebra known as combinatorial group theory, Nielsen transformations are certain automorphisms of a free group which are a non-commutative analogue of row reduction and one of the main tools used in studying free groups (Fine, Rosenberger & Stille 1995).
Affine transformation (Euclidean geometry) Bäcklund transform; Bilinear transform; Box–Muller transform; Burrows–Wheeler transform (data compression) Chirplet transform; Distance transform; Fractal transform; Gelfand transform; Hadamard transform; Hough transform (digital image processing) Inverse scattering transform; Legendre ...
In the context of the Aanderaa–Karp–Rosenberg conjecture on the query complexity of monotone graph properties, Gröger (1992) showed that any subgraph isomorphism problem has query complexity Ω(n 3/2); that is, solving the subgraph isomorphism requires an algorithm to check the presence or absence in the input of Ω(n 3/2) different edges ...
Starting from the graph of f, a horizontal translation means composing f with a function , for some constant number a, resulting in a graph consisting of points (, ()) . Each point ( x , y ) {\displaystyle (x,y)} of the original graph corresponds to the point ( x + a , y ) {\displaystyle (x+a,y)} in the new graph ...
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