Báo cáo toán học: "Improved Upper Bounds for the Laplacian Spectral Radius of a Graph" docx

... degree and the average 2-degree of the vertices. As a matter of fact, we can also utilize other characteristics of the vertex to estimate the Laplacian spectral radius of graphs. The definition of ... is also called the Laplacian spectral radius. Let K(G) = D (G ) + A( G). It is called the signless Laplacian matrix of G (or Quasi -Laplacian) . A semi...

Ngày tải lên: 08/08/2014, 12:23

... exponentially. Fortunately, automating the generation of states and transfer matrices is straightforward as the following algorithm shows: 1. Initalize a set of untreated states with state 0 as the ... determinant of the matrix I − zA where I denotes the identity matrix and A is the state transfer matrix of the automaton. Consequently, the root of smallest modulu...

Ngày tải lên: 07/08/2014, 06:20

... case there are at least 14 edges from A to B and there must be at least 6 of the A v ’s that have cardinality 2. If there were more than 6 the argument for case ( 1a) repeated would show the existence ... =2 for all eight v in B.IfA v 1 A v 2 =∅then A v 1 ∪ A v 2 = A and so {a, b, v 1 ,v 2 } is a dominating set for G. So we can assume that A v 1 ∩ A v 2 = ∅ f...

Ngày tải lên: 07/08/2014, 06:20

... David C Fisher and Anne Spalding, Domination of circulant graphs: an example of min-plus algebra. Proceedings of the Twenty-eighth Southeastern International Conference on Combinatorics, Graph ... obtained a formula for the domination number of the circulant graph C(S, n) as a function of n and S, but results and techniques do not appear to be useful for our purposes....

Ngày tải lên: 07/08/2014, 06:22

... permutation characters of S n are available on programs as Magma [5] or GAP [13]. Using the “linprog” ro utine of Matlab [14], we obtain the bounds in Table 1. Note that the linear programming ... M. Deza and P. Frankl. On the maximum number of permutations with given max- imal or minimal distance. Journal of Combinatorial Theory (A) , 22:352–360, 1977. [11] Michael Deza and...

Ngày tải lên: 08/08/2014, 12:22

... Dowman Drive Emory University, Atlanta GA 30322 Tomasz Luczak Department of Mathematics and Computer Science 400 Dowman Drive Emory University, Atlanta GA 30322 and Department of Discrete Mathematics Faculty ... Graph Lemma 6 For any edge e in the complement of F (n, l) and l ≥ 5, the graph F (n, l)+e contains a cycle of length l. Proof: We divide the proof into the appro...

Ngày tải lên: 07/08/2014, 13:21

... power for which q ≥ k = |R|, we obtain the order of H as appears in (4). Remark. It is easy to see that the diameter of a k-regular graph of order v is at least log k−1 v and that the random ... Ch. X1] these all have small girth. The problem of constructing infinite families of graphs of large girth 8 NEW UPPER BOUNDS ON THE ORDER OF CAGES 1 F. LAZEBNIK Departm...

Ngày tải lên: 07/08/2014, 06:22

... theorem that J(x) ≠ ∅ for any x Î X.Thenthe multi-valued operator J : X ↦ X* is called the normalized duality mapping of X.Recall that a Banach space X is said to be uniformly convex if for each ε ... inequalities. J Math Anal Appl. 251, 217–229 (2000). doi:10.1006/jmaa.2000.7042 7. Xu, B, Noor, MA: Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces....

Ngày tải lên: 20/06/2014, 21:20

... when the number of relays is relatively large, the gain of ergodic capacity is co nstant, approximately. Take the symmetric channels as example, at SNR = 10 dB, the gain of the upper bound of ergodic ... University of Posts and Telecommunications, Nanjing 210003, China Full list of author information is available at the end of the article Jia et al. EURASIP Journ...

Ngày tải lên: 20/06/2014, 21:20

... mathematical philosophies. The mathematical community could benefit greatly from more mathematicians like him. I would also like to thank Brendan McKay for his assistance and the referee for calling ... 344 the electronic journal of combinatorics 6 (1999), #R3 6 [GG] R. Greenwood and A. Gleason, Combinatorial Relations and Chromatic Graphs, Canadian Journal of Mathematics, 7, 19...

Ngày tải lên: 07/08/2014, 06:20