Cayley graph
E911229
A Cayley graph is a graphical representation of a group where vertices correspond to group elements and edges represent multiplication by chosen generators, widely used in group theory and geometric group theory.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
construction in group theory
ⓘ
graph theory concept ⓘ mathematical object ⓘ |
| appliedIn |
combinatorial group theory
ⓘ
geometric group theory ⓘ interconnection networks in parallel computing ⓘ network design ⓘ |
| constructionOf |
finite group
ⓘ
finitely generated group ⓘ infinite group ⓘ |
| dependsOn | choice of generating set ⓘ |
| edgeCondition | edge from g to gs for g in G and s in S ⓘ |
| field |
geometric group theory
ⓘ
graph theory ⓘ group theory ⓘ |
| generalizationOf |
cycle graph of cyclic group
ⓘ
dihedral group graphs ⓘ hypercube graph of (Z2)^n ⓘ |
| hasAutomorphismGroup | contains left-regular representation of group ⓘ |
| hasEdgeDefinition | edges connect elements differing by a generator ⓘ |
| hasNotation | Cay(G,S) ⓘ |
| hasProperty |
can be colored by generators
ⓘ
can be directed or undirected ⓘ connected if generating set generates the group ⓘ edge-colorable by generators ⓘ encodes word metric of group ⓘ locally finite if generating set is finite ⓘ quasi-isometry invariant up to generating set choice ⓘ regular graph ⓘ vertex-transitive graph ⓘ |
| hasVertexSet | underlying group ⓘ |
| isUndirectedIf | generating set is symmetric ⓘ |
| namedAfter | Arthur Cayley NERFINISHED ⓘ |
| parameter |
generating set S
ⓘ
group G ⓘ |
| relatedTo |
Cayley complex
NERFINISHED
ⓘ
Cayley digraph NERFINISHED ⓘ Cayley table NERFINISHED ⓘ Schreier graph ⓘ |
| specialCaseOf | vertex-transitive graph ⓘ |
| usedFor |
studying automorphism groups of graphs
ⓘ
studying expander graphs ⓘ studying finitely generated groups ⓘ studying growth of groups ⓘ studying random walks on groups ⓘ studying spectral properties of groups ⓘ studying symmetry ⓘ studying word metrics on groups ⓘ visualizing group structure ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.