Báo cáo toán học: "Automorphism groups of Cayley digraphs of Z3 p" potx

... these digraphs are also Cayley digraphs of the generalized quaternion group of order 2 k+1 .Inthis case, these digraphs are non-normal Cayley digraphs of the generalized quaternion group of order ... orbital digraphs of G to the set of sub-orbits of G (for fixed ω ∈ Ω). Definition 1.3 Let G be a transitive permutation group of degree mk that admits a complete block...

Ngày tải lên: 07/08/2014, 07:21

... groups of all of these orbital digraphs, and as the 2-closure is the intersection of the automorphism groups of all orbital digraphs, we have that G (2) = S 3 ≀ S p . This completes the proof of ... will give a description of the automorphism group of a Cayley digraph of Z 3 p , p an odd prime. The automorphism groups of Cayley digraphs have been determined for...

Ngày tải lên: 08/08/2014, 01:20

... proceed with the proof of the theorem. Proof. Let Q be a partition of the vertices of D into sets of vertices, each of which induces a connected component of the k-complement of D. Then we let ... there a Cayley (di)graph Γ of Z p × Z p 2 which can be written as a wreath product of a Cayley (di)graph of Z p and a Cayley (di)graph of Z p 2 and can also be written as...

Ngày tải lên: 07/08/2014, 21:21

... primitive normal Cayley graphs of some classes of groups. The purpose of t his paper is to give a complete chara cterization of locally primitive normal Cayley graphs of metacyclic groups. For convenience, ... subgroup of index 2 which is normal in X, then Γ is called an X-bi-normal Cayley graph of G. For a group H, recall the socle of H, denoted by soc(H), is the pro...

Ngày tải lên: 08/08/2014, 01:20

... automorphism groups of trees are fully understood [Ser80]. Let G T be the class of groups that are represented by the automorphism groups of trees and G F represented by automorphisms of forests 2 . ... pairs of groups in G T delete to each other? Another interesting aspect of our construction is that the resulting graphs are very large, with the order of the graphs cubi...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 15:20

... edge-connectivity of its unitary Cayley graph. Then κ(G R ) = κ ′ (G R ) = |R ∗ |. Proof. We argue following the reasoning in [9], Theorem 4. According to a theorem of Watkins [10], the vertex connectivity of ... unitary Cayley graphs have been studied as objects of independent interest (see, for example, [2], [3], [7], [8], [9]) but are of particular relevance in the study of...

Ngày tải lên: 08/08/2014, 01:20

... eleven infinite families of tetravalent no n-normal Cayley graphs of order 4p including two infinite families of Cayley graphs on abelian groups, one infinite family of Cayley graphs on the dicyclic ... disconnected normal Cayley graphs. For this reason, it suffices to consider the connected ones when one investigates the normality of Cayley graphs. One of the standard probl...

Ngày tải lên: 08/08/2014, 01:20

Ngày tải lên: 05/08/2014, 15:20

... to that of the MNP-PEI due to the presence of -OH groups on the particle surface which is due to the PEG coating (MNP-PEI-PEG) [see Table S1 in Additional file 1]. Cellular uptake of nanoparticles ... damage. These findings highlight the importance of assay selection and of dissection of different cellular responses in in-vitro characterisation of nanostructures. Keyw...

Ngày tải lên: 20/06/2014, 20:20