Cayley graph - Wikipedia
WEBA Cayley graph is a graph that encodes the abstract structure of a group using a specified set of generators. Learn the definition, examples, characterization, and applications of Cayley graphs in combinatorial and geometric group theory.
WEBLearn how to construct Cayley graphs and use them to study various kinds of groups. This lecture covers free groups, group presentations, cosets, and examples of Cayley graphs.
Cayley Graph -- from Wolfram MathWorld
WEBAug 22, 2024 · A Cayley graph is a directed graph associated with a group and a set of generators, where there is an edge between two vertices if the corresponding group elements are related by a generator. Learn how to compute Cayley graphs, see some common types and classes of Cayley graphs, and explore their applications and properties.
WEBLearn about Cayley graphs, which are graphs whose vertices are the elements of a group and whose edges are determined by a set of generators. See how to compute the eigenvalues of Cayley graphs over Abelian groups, such as ring graphs and hypercubes, and how to use them for spectral graph theory.
WEBTopology is concerned with the continuous deformations, such as shrinking, stretching, or twisting, of objects. This section establishes some elementary con-cepts in algebraic topology, which uses algebraic structures, such as groups, to FIGURE 3.
WEBLearn what a Cayley graph is and how it encodes information about a group with a finite generating set. See examples of Cayley graphs for various groups, such as S3, D4 and F2, and how they relate to symmetry groups, trees and free groups.
WEBLearn about Cayley graphs, which are regular and vertex-transitive graphs associated to finite groups and generating sets. Explore their expansion properties, eigenvalues, representation theory and applications to number theory.
WEBLearn how to construct Cayley graphs of groups and how to use their spectrum to prove graph properties. See examples of triangle-free graphs with no large independent sets and their applications to Ramsey theory.
WEBLecture 6. In which we talk about the spectrum of Cayley graphs of abelian groups, we compute the eigenvalues and eigenvectors of the cycle and of the hypercube, and we verify the tightness of the Cheeger inequalities and of the analysis of spectral partitioning. In this lecture we will prove the following results:
WEBCayley graph is a colored graph, which was introduced by Cayley in 1878 as a graphic representation of abstract groups. A group is a set of elements together with an operation that combines any two of its elements to form a third element.