Graph Characteristics of Particular Group Families
Certain group types give typical graphs:
- Cyclic groups Zn is a single cycle graphed simply as an n-sided polygon with the elements at the vertices.
| Z1 | Z2 | Z3 | Z4 | Z5 | Z6 | Z7 | Z8 |
|---|
- When n is a prime number, groups of the form (Zn)m will have (nm-1)/(n-1) n-element cycles sharing the common identity element.
| Z2² | Z2³ | Z24 | Z3² |
|---|
- Dihedral groups Dihn consists of an n-element cycle and n 2-element cycles.
| Dih1 | Dih2 | Dih3 | Dih4 | Dih5 | Dih6 | Dih7 |
|---|
- Symmetric groups - The symmetric group Sn contains, for any group of order n, a subgroup isomorphic to that group. Thus the cycle graph of every group of order n will be found in the cycle graph of Sn. See example: Subgroups of S4
Read more about this topic: Cycle Graph (algebra)
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