GRAPH (Group of a)
Charles François (2004). GRAPH (Group of a), International Encyclopedia of Systems and Cybernetics, 2(1): 1463.
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 1463 ▶ |
| Object type | Methodology or model |
- “The collection of all its automorphisms” (F. HARARY, 1967, p.25).
Different graphs can be topologically isomorphic, and thus reunited through a group.
F. HARARY writes: “It is a permutation group acting on the set of points (nodes). It is known (FRUCHT, 1949) that every finite group is abstractly isomorphic to the group of some graph” (Ibid).
This author also defines the line (edge) group of a graph: “The permutation group whose objects are the lines of G and whose permutations are induced by those of the group of automorphisms” (Ibid).