منابع مشابه
On 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.
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It is proved that each 2-element generating set of A5 is a CI-subset and that the corresponding Cayley digraph is normal. It is furthermore proved that for each 3-element generating set of A5 the corresponding Cayley digraph is normal.
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Let Cd,k be the largest number of vertices in a Cayley digraph of degree d and diameter k, and let BCd,k be the largest order of a bipartite Cayley digraph for given d and k. For every degree d ≥ 2 and for every odd k we construct Cayley digraphs of order 2k ( ⌊d2⌋ )k and diameter at most k, where k ≥ 3, and bipartite Cayley digraphs of order 2(k − 1) ( ⌊d2⌋ )k−1 and diameter at most k, where k...
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We call a Cayley digraph X = Cay(G, 8) normal for G if the right regular representation R( G) of G is normal in the full automorphism group Aut(X) of X. In this paper we determine the normality of Cayley digraphs of groups of order twice a prime.
متن کاملOn the normality of Cayley digraphs of valency 2 on non-abelian groups of odd square free order
In this paper, we prove that all Cayley digraphs of valency 2 on nonabelian groups of odd square-free order are normal. For a given subset S of a finite group G without the identity element 1, the Cayley digraph on G with respect to S is denoted by r =Cay(G, S) where V(r) = G, E(r) = {(g, 8g) I 9 E G,8 E S}. It is clear that Aut (r), the automorphism group of r, contains the right regular repre...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2015
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.10.019