In the area of abstract algebra known as group theory, the diameter of a finite group is a measure of its complexity.
Consider a finite group , and any set of generators S. Define to be the graph diameter of the Cayley graph . Then the diameter of is the largest value of taken over all generating sets S.
For instance, every finite cyclic group of order s, the Cayley graph for a generating set with one generator is an s-vertex cycle graph. The diameter of this graph, and of the group, is . [1]
It is conjectured, for all non-abelian finite simple groups G, that [2]
Many partial results are known but the full conjecture remains open. [3]
In the area of abstract algebra known as group theory, the diameter of a finite group is a measure of its complexity.
Consider a finite group , and any set of generators S. Define to be the graph diameter of the Cayley graph . Then the diameter of is the largest value of taken over all generating sets S.
For instance, every finite cyclic group of order s, the Cayley graph for a generating set with one generator is an s-vertex cycle graph. The diameter of this graph, and of the group, is . [1]
It is conjectured, for all non-abelian finite simple groups G, that [2]
Many partial results are known but the full conjecture remains open. [3]