Báo cáo toán học: "Integral Cayley graphs over abelian groups" pps

... noticed by Lov´asz [12] that all Cayley graphs over Z n 2 (“cubelike graphs ) are integral. The fo llowing theorem extends this result. Theorem 13. All nontrivial abelian C ayley integral groups ... 17 (2010), #R81 9 A finite group Γ is called Cayley integral, if every undirected Cayley graph over Γ is integral. We show that all nontrivial abelian Cayley integral groups are...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 09:46

... integral Cayley graphs and introduce some infinite family of connected integ r al Cayley graphs. The main results are the following. Theorem 1.1 There are exactly seven connected cubic integral Cayley ... characters of the underlying group, we give some infinite families of integral Cayley graphs. The study of Cayley graphs of the symmetric group generated by tra nspositions i...

Ngày tải lên: 08/08/2014, 01:20

... theorem of N. Alon and Y. Roichman [4] asserts that random Cayley graphs are expanders. Specifically, they study the spectrum of the Cayley graphs obtained by selecting k elements, independently and ... sums   g α g · g | α g ∈ C  the electronic journal of combinatorics 11 (2004), #R62 3 Random Cayley graphs are expanders: a simple proof of the Alon–Roichman theorem ZEPH LANDAU...

Ngày tải lên: 07/08/2014, 08:20

... and Stiebitz [13] proved it to be true for line graphs of multigraphs, while Balogh et al. [1] proved it to be true for quasi-line graphs and for graphs with independence number 2. the electronic ... open. 8 Double-edge-critical graphs and mixed-double- critical graphs A natural variation on the theme of double-critical graphs is to consider double-edge- critical graphs. A vertex...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 15:20

... of length greater than k. We then generalize this to other expectations over the unitary group, as well as expectations over the orthogonal and symplectic groups. In each case, the expectations ... =l≤k   e iθ j − e iθ l   (see, for example, [16]), we can immediately rewrite I(n, k) as an expectation over U(k): I(n, k)=(2π) k k!E U∈U(k)       1≤j≤k cos(θ j )   2n    . Wr...

Ngày tải lên: 07/08/2014, 06:22

... log 2 n = k. This completes the proof. ✷ For any finite abelian group G, we have the following theorem. Theorem 2.5 Let G be a finite abelian group. Then for every k ∈ [L(G), d ∗ (G)], there exists ... that is  (S) = G\{0}. For any finite abelian group G, it is obvious that the maximal size of an unextendible sequence is D(G) − 1. Definition 1.2 For a finite abelian group G, we define u(...

Ngày tải lên: 07/08/2014, 15:22

... arbitrary constant t 0 . Moreover, the bounds obtained from Theorems 12 and 13 match with the bounds obtained by code graphs in Theorem 3.1 in [2]. These graphs are Caley graphs and their construction ... non-Euclidean spaces and Ramanujan graphs, European Journal of Combinatorics 25 (2004), 243-259. [8] E. Bannai, O. Shimabukuro, H. Tanaka, Finite Euclidean graphs and Ramanujan gra...

Ngày tải lên: 07/08/2014, 15:22

... have I (k) = I k if every vertex cover c of order k can be decomposed as a sum of k vertex cover of order 1 of Δ. Every integral vector c ∈ N r is a vertex cover of some order k ≥ 0. The minimum ... Fulker- sonian hypergraphs are generalizations of Mengerian hypergraphs. Unlike the Mengerian property, the Fulkersonian property is preserved by passing to the hypergraph of minimal vertex covers...

Ngày tải lên: 06/08/2014, 05:20