Explore: Cayley Graphs

The structure and symmetry of Cayley graphs make them particularly good candidates for constructing expander graphs. Let G {\displaystyle G} be a group

Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric

vertex-transitive graphs with no Hamiltonian cycles is a Cayley graph. This observation leads to a weaker version of the conjecture: Every finite connected Cayley graph

vertex-transitive graphs on at most 1280 vertices. Although every Cayley graph is vertex-transitive, there exist other vertex-transitive graphs that are not Cayley graphs

retrieved 2013-11-26 Alspach, Brian (1997), "Isomorphism and Cayley graphs on abelian groups", Graph symmetry (Montreal, PQ, 1996), NATO Adv. Sci. Inst. Ser

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

Coxeter graph and two graphs derived from the Petersen and Coxeter graphs by replacing each vertex with a triangle. If G is a 2-connected, r-regular graph with

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

Ramanujan graphs "fuse diverse branches of pure mathematics, namely, number theory, representation theory, and algebraic geometry". These graphs are indirectly

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