In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract...

graphs (such as the Petersen graph, the Heawood graph and the vertices and edges of the Platonic solids). The finite Cayley graphs (such as cube-connected...

graph, such as the Petersen graph, has few distinct values (the Petersen graph has 3, which is the minimum possible, given its diameter). For Cayley graphs...

Cayley graph is a cycle graph, and for an infinite cyclic group with its generator the Cayley graph is a doubly infinite path graph. However, Cayley graphs...

graph. Despite its high degree of symmetry, the Petersen graph is not a Cayley graph. It is the smallest vertex-transitive graph that is not a Cayley...

theory, Cayley tables, Cayley graphs, and Cayley's theorem are named in his honour, as well as Cayley's formula in combinatorics. Arthur Cayley was born...

defines a covering map of Cayley graphs φ* : Γ(F) → Γ(G), in fact a universal covering. Hence, the fundamental group of the Cayley graph Γ(G) is isomorphic to...

Cayley graph that can itself be embedded on the double torus, and was shown by Tucker (1984) to be the unique group with genus two. The Cayley graph on...

directed Cayley graph of an abelian group has a Hamiltonian path; however, every cyclic group whose order is not a prime power has a directed Cayley graph that...

In mathematics, Cayley's formula is a result in graph theory named after Arthur Cayley. It states that for every positive integer n {\displaystyle n} ...

as a graph, is Hamiltonian The Cayley graph of a finite Coxeter group is Hamiltonian (For more information on Hamiltonian paths in Cayley graphs, see...

graph of degree d, we have: 2(d + 1)/3 ≤ κ(G) ≤ λ(G) = d. For a vertex-transitive graph of degree d ≤ 4, or for any (undirected) minimal Cayley graph...

was coined in 1857 by the British mathematician Arthur Cayley. A tree is an undirected graph G that satisfies any of the following equivalent conditions:...

right shows the Cayley graph of S4. Its edge colors represent the 3 generating transpositions: (1, 2), (2, 3), (3, 4) This Cayley graph is Hamiltonian;...

S=-S} . Then the Cayley graph for F q {\displaystyle \mathbb {F} _{q}} with generators from S {\displaystyle S} is a Ramanujan graph. Mathematicians are...

extension on this graph. It is an integral Cayley graph. On a Sudoku board of size n 2 × n 2 {\displaystyle n^{2}\times n^{2}} , the Sudoku graph has n 4 {\displaystyle...

bipartite graph Disperser Expander Extractor Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement...

topological spaces associated with the graph. Ends of graphs may be used (via Cayley graphs) to define ends of finitely generated groups. Finitely generated infinite...

Cayley graph of the quaternion group embedded in the torus. The Pappus graph and associated map embedded in the torus. Planar graph Topological graph...

vertex set. A directed cycle graph has uniform in-degree 1 and uniform out-degree 1. Directed cycle graphs are Cayley graphs for cyclic groups (see e.g...

concern the enumeration of graphs with particular properties. Enumerative graph theory then arose from the results of Cayley and the fundamental results...

examples of highly expanding graphs. Algebraic constructions based on Cayley graphs are known for various variants of expander graphs. The following construction...

total of 120 different points. The truncated dodecadodecahedron forms a Cayley graph for the symmetric group on five elements, as generated by two group members:...

be its Cayley graph with respect to some finite set S {\displaystyle S} of generators. The set X {\displaystyle X} is endowed with its graph metric (in...

{\displaystyle G(10,2)} and the Desargues graph G ( 10 , 3 ) {\displaystyle G(10,3)} . The Nauru graph is a Cayley graph of S4, the symmetric group of permutations...

Seidel [de] as the coset graph of the ternary Golay code. This graph is the Cayley graph of an abelian group. Among abelian Cayley graphs that are strongly regular...

single edge. As with many vertex-transitive graphs, the prism graphs may also be constructed as Cayley graphs. The order-n dihedral group is the group of...

generate families of graphs that (like the Petersen graph) are vertex-transitive but are not Cayley graphs: if G is an edge-transitive graph that has at least...

result in the study of (n,d,λ)-graphs. A Bethe graph of even coordination number 2n is isomorphic to the unoriented Cayley graph of a free group of rank n...

were George Pólya, Arthur Cayley and J. Howard Redfield. In some graphical enumeration problems, the vertices of the graph are considered to be labeled...