A necessary and sufficient condition is given for two Cayley digraphs X 1 = Cay(G 1 , S 1 ) and X 2 = Cay(G 2 , S 2 ) to be isomorphic, where the groups G i are nonisomorphic abelian 2-groups, and the digraphs X i have a regular cyclic group of automorphisms. Our result extends that of Morris [J Gra
Isomorphic Cayley graphs on nonisomorphic groups
β Scribed by Morris, Joy
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 349 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
The issue of when two Cayley digraphs on different abelian groups of prime power order can be isomorphic is examined. This had previously been determined by Anne Joseph for squares of primes; her results are extended.
π SIMILAR VOLUMES
Let G be a finite group, S a subset of G=f1g; and let Cay Γ°G; SΓ denote the Cayley digraph of G with respect to S: If, for any subset T of G=f1g; CayΓ°G; SΓ ffi CayΓ°G; T Γ implies that S a ΒΌ T for some a 2 AutΓ°GΓ; then S is called a CI-subset. The group G is called a CIM-group if for any minimal gene
A Cayley graph Cay(G, S) of a group G is called a CI-graph if whenever T is another subset of G for which Cay(G, S) βΌ = Cay(G, T ), there exists an automorphism Ο of G such that S Ο = T . For a positive integer m, the group G is said to have the m-CI property if all Cayley graphs of G of valency m a
A Cayley graph or digraph Cay(G, S) of a finite group G is called a CI-graph of G if, for any T/G, Cay(G, S)$Cay(G, T) if and only if S \_ =T for some \_ # Aut(G). We study the problem of determining which Cayley graphs and digraphs for a given group are CI-graphs. A finite group G is called a conne
Let G be a finite group, and let Cay(G, S) be a Cayley digraph of G. If, for all T β G, Cay(G, S) βΌ = Cay(G, T ) implies S Ξ± = T for some Ξ± β Aut(G), then Cay(G, S) is called a CI-graph of G. For a group G, if all Cayley digraphs of valency m are CI-graphs, then G is said to have the m-DCI property;