Isomorphisms and automorphism groups of a class of Cayley digraphs on Abelian groups
نویسنده
چکیده
In this paper, we investigate problems about isomorphisms and automorphism groups of Cayley digraphs. A class of Cayley digraphs, corresponding to the so-called CDI-subsets, for which the isomorphisms are uniquely determined by the group automorphisms is characterized. Their automorphism groups are also characterized.
منابع مشابه
NORMAL 6-VALENT CAYLEY GRAPHS OF ABELIAN GROUPS
Abstract : We call a Cayley graph Γ = Cay (G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aut(Γ). In this paper, a classification of all non-normal Cayley graphs of finite abelian group with valency 6 was presented.
متن کاملON THE NORMALITY OF t-CAYLEY HYPERGRAPHS OF ABELIAN GROUPS
A t-Cayley hypergraph X = t-Cay(G; S) is called normal for a finite group G, if the right regular representationR(G) of G is normal in the full automorphism group Aut(X) of X. In this paper, we investigate the normality of t-Cayley hypergraphs of abelian groups, where S < 4.
متن کاملAutomorphisms of groups and isomorphisms of Cayley digraphs
Let G be a graph and S a subset of G not ,",VLLCU,lJ.HHF-, element of The of G with respect to is a directed graph with vertex set G and for x and y in there is an arc from x to y if and only if x-1y E S. In this paper, we discuss the between the isomorphisms of D(G, S) and the automorphisms of G. The results to studying the and automorphisms of hierarchical digraphs of abelian groups. For any ...
متن کاملAsymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order
We show that almost every Cayley graph Γ of an abelian group G of odd prime-power order has automorphism group as small as possible. Additionally, we show that almost every Cayley (di)graph Γ of an abelian group G of odd prime-power order that does not have automorphism group as small as possible is a normal Cayley (di)graph of G (that is, GL/Aut(Γ)).
متن کاملOn the Normality of Some Cayley Digraphs with Valency 2
We call a Cayley digraph Γ = Cay(G,S) normal for G if R(G), the right regular representation of G, is a normal subgroup of the full automorphism group Aut(Γ) of Γ. In this paper we determine the normality of Cayley digraphs of valency 2 on the groups of order pq and also on non-abelian finite groups G such that every proper subgroup of G is abelian.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 15 شماره
صفحات -
تاریخ انتشار 1997