Báo cáo toán học: "The diameter and Laplacian eigenvalues of directed graphs" pps

... factor of 4 of the bound for the undirected case. We have now seen that the eigenvalues of the Laplacian can be used to control the diameter of the graph. It is also known that the eigenvalues of ... for the rate of convergence in terms of λ? Another important consequence of the Laplacian eigenvalues is its relationship with the Cheeger constant of a directed g...

Ngày tải lên: 07/08/2014, 13:21

... transpose of P . The Laplacian satisfies L ∗ = L, that is, the Laplacian is symmetric. The spectrum of a graph is the eigenvalues and eigenfunctions of the Laplacian of the graph. We give an extension of ... the combinatorial Laplacian. In [1] and [3], the definition of the combinatorial Laplacian is given. Also, graph coverings are used for the calculation of the...

Ngày tải lên: 07/08/2014, 21:21

... the height of GaSb/In 0.53 Ga 0.47 As QDs. (a) The AFM image of GaSb/In 0.53 Ga 0.47 As QDs, (b) histogram of the height of GaSb/In 0.53 Ga 0.47 As QDs, and (c) the STEM image of GaSb/In 0.53 Ga 0.47 As ... dependence of the PL peak energies over the third root of the excitation density [20]. The inset of Figure 3b shows the linear dependence of the PL peak energies...

Ngày tải lên: 20/06/2014, 20:20

... Project, the PCSIRT Project of the Ministry of Education, the Ministry of Science and Technology, and the National Science Foundation of China. the electronic journal of combinatorics 14 (2007), ... the number of relative derangements on [n], and let D n denote the number of the derangements on [n]. The following relation is well-known, see Brualdi [2, Theorem 6.5.1], or A...

Ngày tải lên: 07/08/2014, 15:22

... disjoint union of a 9-cycle and a triangle, 3. the disjoint union of two 6-cycles, 4. the disjoint union of a 6-cycle and two triangles, 5. the disjoint union of four triangles. One method of classifying ... subgraph, using the eigenvalues of the SRG to limit the number of possibilities. We make the observation that Γ has eigenvalues 12 1 , 2 24 and −4 15 (exponents de...

Ngày tải lên: 07/08/2014, 06:20

... necessity and in this regard, plant essential oils may offer a great potential and hope. Several studies have reported the efficacy of antibacterials obtained from the essential oils of various ... the best of the authors’ knowledge, there are no reports about the chemical content and biological effect of the essential oils of L. resedifolia. There no reports on the essenti...

Ngày tải lên: 20/06/2014, 20:20

... of some bioactive compounds such as ß-lactams [16–18], and employed as ligands for the complexation of metal ions [19]. SBs and their complexes are largely studied because they interested and ... functional group of IMHC. The appearance of a broad strong band in the IR spectra of IMHC in 3421 cm –1 is assigned to N–H stretching vibrations of the primary amine group. The...

Ngày tải lên: 20/06/2014, 20:20

... calculation of the character of S n on the homology of the order complex of L A col , s n and using a formula of Orlik & Solomon [10] we are able to describe the character of S n on the cohomology of ... Π col,s n , s ≥ 1, be the set of all pairs (τ = B 1 |···|B t ,(l 1 , ,l t )) of partitions τ ∈ Π n and sequences of numbers l i ∈{0, ,s }of length t,wheretis the...

Ngày tải lên: 07/08/2014, 06:20

... inductive proof of the determinant evaluation in Theorem 10 (and also of its q-analogue in [9]), and could also be used to give an inductive proof of the determinant evaluation in Theorem 8 (and its ... determinant of size at most 2t +1,asis elaborated in Step 6 of the proof, and since a polynomial of degree ≤m/2 is uniquely determined by its values at m/2 +1 distinct po...

Ngày tải lên: 07/08/2014, 06:20

... about the diameter of directed graphs. Most bounds on the diameter of undirected graphs do not have a straightforward analogue for directed graphs. A case in point, and the starting point of our ... 1, where n is the order of D. Proof. Let D be the directed graph of order n obtained from the disjoint union of two copies H 1 and H 2 of the complete digraph K ( δ 2 )...

Ngày tải lên: 08/08/2014, 12:23