Báo cáo toán học: "The Scattering Matrix of a Graph" pps

... 05C83 Abstract The arc-representation of a graph is a mapping from the set of vertices to the arcs of a circle such that adjacent vertices are mapped to intersecting arcs. The width ofsucharepresentationisthemaximumnumberofarcshavingapointincommon. The ... set of arcs of a base circle, such that adjacent vertices of G are mapped to intersecting arcs. The width (in a repr...

Ngày tải lên: 07/08/2014, 06:22

... graphs. Encyclopedia of Mathematics and its Applications, 66. Cambridge University Press, Cambridge, 1997. [4] N. Deo, F. Harary and A. J. Schwenk, An Eigenvector Characterization of Cospectral Graphs ... subgraphs of G is known as its deck. The characteristic polynomial of G is the characteristic polynomial of its adjacency matrix A and is defined by P G (x)=det(xI − A) . We c...

Ngày tải lên: 07/08/2014, 06:20

... recoverable using any algorithm designed to compute the product of an adjacency matrix of the graph and an arbitrary vector. The linear complexity of a graph may therefore be seen as a measure of ... complexity of a graph Γ is a measure of how hard it is to compute AX,whereA is an adjacency matrix of Γ and X is a generic vector of the appropriate size. the electr...

Ngày tải lên: 07/08/2014, 13:21

...

Ngày tải lên: 05/08/2014, 10:20

... itself a right translation of S if (ab)ρ = a( bρ) for all a, b ∈ S. A left translation λ and a right translation ρ of S are said to be linked if a( λb)= (a )b for all a, b ∈ S. In this case, we call ... investigated the translational hull of a type -A semigroup, in particular, the result obtained by Ault [1] was sub- stantially generalized and extended. Thus, the translatio...

Ngày tải lên: 06/08/2014, 05:20

... we know that the most typical examples of basic Hopf algebras of finite representation type are Taft algebras and the dual of A( n, d, μ, q), which as an associative algebra is generated by two ... algebra is a kind of generalization of gener- alized Taft algebra and of course Taft algebra. Therefore, it is natural to ask the following question: whether is the quantum double of...

Ngày tải lên: 06/08/2014, 05:20

... Handbook of Mathematical Functions,NationalBureauof Standards, Washington DC, 1972. 2. P. Erd˝os and P. Tur´an, On some problems of a statistical group theory, III,, Acta Math. Acad. Sci. Hungar. ... greater than √ n sincewemayalwaystakep = q) we may halve the distance from m to n by one application of this inequality. After at most log 2 n applications of the above inequality we ob...

Ngày tải lên: 07/08/2014, 06:22

... of Mathematical Sciences State University of New York Binghamton, NY 13902–6000, USA matthias@math.binghamton.edu Ira M. Gessel ∗ Department of Mathematics Brandeis University Waltham, MA 02454–9110, ... derive an explicit formula for the polynomial part of p A . Let A = {a 1 , ,a n } be a set of positive integers with gcd (a 1 , ,a n )=1. The classical Frobenius problem a...

Ngày tải lên: 07/08/2014, 06:22

... c(n)isthe number of length n factors of F that can be followed by both a 0 and a 1 in F . Definition. Following standard terminology, define a factor w of F to be special if both w0andw1 are factors of F .Ifw ... ∈ >0 .DenotingA =  ∞ i=1 A i and B =  ∞ i=1 B i ,wehaveA ∪ B = >0 ,and A ∩ B = ∅. Fraenkel [9] generalized the classical Wythoff game (s = t =1)tothecases =1,t...

Ngày tải lên: 07/08/2014, 06:23

... Bruhat intervals have the same a ne span. Theorem 6.2. The set of cd-indices of Bruhat intervals spans the a ne space of cd- polynomials. Proof. The space of cd-polynomials of degree n − 1 has ... then P  is graded and thin, and maximal chains in P  have the same length as maximal chains in P . Proof. Suppose P is graded and thin and let C  be a maximal chain in P  .ThenC ...

Ngày tải lên: 07/08/2014, 08:22