Báo cáo toán hoc:" Locally primitive normal Cayley graphs of metacyclic groups" potx

... study locally 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 ... construct three types of Cayley graphs (see Constructions 4.1-4.3 below). The second main theorem of this paper is to prove that all locally primitive...

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 sta...

Ngày tải lên: 08/08/2014, 01:20

... 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 ... faithful representation of Aut(Γ) and Γ is not a Cayley graph. In this paper, we give examples of vertex-transitive digraphs that are Cayley di- graphs and the action of...

Ngày tải lên: 07/08/2014, 07:21

... 1. The final part of this section is devoted to the proof of Theorem 1.3. From now on we shall assume that n = m m , m ≥ 4 and a is the product of m pairwise disjoint cycles each of length m. Given ... d(x, y) ≤ f(m). Proof of Theorem 1.3 Write x as an m ×m array with the rows being the cycles of x. Any permutation which leaves the set of rows fixed produces an element y of X wi...

Ngày tải lên: 07/08/2014, 21:21

... 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 graph the electronic journal of ... Sinz. Longest induced cycles in Cayley graphs. ArXiv: math/0410308v2 (2004). [9] W. Klotz and T. Sander. Some Properties of Unitary Cayley Graphs. Electronic Journal of C...

Ngày tải lên: 08/08/2014, 01:20

... the analysis of this section in our characterization both of the diameters of the graphs G n , and of the factors of n for G n a perfect graph. As T n is a multiplicative subgroup of Z × n , we ... restricted variant of unitary Cayley graphs modulo n, an d implications for a decomposition of elements of symplectic operators over the integers modulo n. We defin e quadrat...

Ngày tải lên: 08/08/2014, 12:22

... monotonicity of f(δ) in the required range, and completes the proof of the theorem. ✷ References [1] A. Alon, S. Hoory, N. Linial, A Continuous Analogue of the Girth Problem, Journal of Combinatorial ... electronic journal of combinatorics 14 (2007), #N1 4 Maximum matchings in regular graphs of high girth Abraham D. Flaxman Microsoft Research Redmond, Washington, USA abie@micros...

Ngày tải lên: 07/08/2014, 13:21

... journal of combinatorics 14 (2007), #R43 16 (and easy to see) that the spectrum of any Schreier graph X(G/H, T ) is a subset of the spectrum of the Cayley graph X(G/T ), hence if a collection of Cayley ... (elements of S are the “open dots”) Proof. The proof is straightforward (using, for example, the “balls in boxes” interpretation as in the proof of Proposition 3.1.) We sk...

Ngày tải lên: 07/08/2014, 15:22

... number of par- titions of [n] containing exactly k blocks where k is fixed according to the number of o ccur rences of a subword pattern τ for several classes of patterns, includ ing all words of ... Stirling number of the second kind. We now provide a combinatorial proof of Corollary 2.12. By Lemma 2.5, to complete the proof, we must show that the total number of non-primary...

Ngày tải lên: 08/08/2014, 11:20

Ngày tải lên: 05/08/2014, 09:46