Cayley Graph Generator. A minimum generating set for Z 8 would have only. Group elements are represented as vertices and generators are represented as directed edges.
A minimum generating set for Z 8 would have only. Video shows what Cayley graph means. Remark Figure 3 illustrates that a non-minimal generating set for a group can be used in a Cayley-graph speci cation of a graph.
Mouse over a vertex to see the permutation Two vertices g and h are connected by an edge if there is a generator in S that multiplies g into h or vice versa.
An arbitrary graph Gis said to be a Cayley graph if there ex-ists a group Band a generating set Xsuch that Gis isomorphic to the Cayley graph for Band X. The smallest vertex-transitive non-Cayley graph is the Petersen graph McKay and Praeger 1994 and the smallest disconnected vertex-transitive non-Cayley graph is two copies of. Jul 10 2010 For instance in a large cyclic group with a single generator the Cayley graph looks one-dimensional and balls grow linearly in until they saturate the entire group whereas with two generators chosen at random the Cayley graph looks two-dimensional and the balls typically grow quadratically until they saturate the entire group. This is a Cayley graph we label each of these edges with the generator that created that edge.
