Báo cáo toán học: "On the functions with values in [α(G), χ(G)]" docx

... we are interested in the following question: can we use the functions θ(G),r(G)andd(G )in( 1)insteadofr + (G)? In the common case the answer is negative. The proof is based on the following lemmas. Lemma ... We are interested in studying the functions of the graph G whose values belong to the interval [α(G), χ(G)]. Here α(G) is the size of the largest sta...

Ngày tải lên: 07/08/2014, 08:20

... + 1 then C is non-singular in P 2 (C). If m − n ≥ 2 then the point (1 : 0 : 0) is a unique singular point of C in P 2 (C).  From Lemma 3.1, the only possible singularities of the curve C in P 2 (C)\[Z ... β j of Q  , then we have the following assertions (i) If n = m or n = m +1 then C is non-singular in P 2 (C). (ii) If n − m ≥ 2 then the point (0 : 1 : 0) is a unique sin...

Ngày tải lên: 06/08/2014, 05:20

... =(V,E)constitutesadominating set if each v ∈ V is either in γ or is adjacent to a vertex in γ.Thedomination number D of G is the size of a dominating set of smallest cardinality. Domination has been the subject ... point concentration for the domination number with probability one. The main results are proved using the second moment method together with the Borel Cantelli...

Ngày tải lên: 07/08/2014, 06:22

... ≥ 3. All matchings of P k , where the vertex k is not in the matching, generate the polynomial p k−1 (x). All matchings of P k , where the vertex k is in the matching, generate the polynomial ... ∅ then we are in the case 1. If B 2 = ∅ then we have either the case 2b with l = k + 1 or the case 2c with l = k + 2 and F = F 1 . Assume now that G has cycles. If B 2 = B...

Ngày tải lên: 07/08/2014, 21:20

... surprising that this remains true within the more general setting of simple families of increasing trees. 3 Generalization Our bijection can be generalized further to prove the following: Theorem ... 05C05 60C05 Abstract By a theorem of Dobrow and Smythe, the depth of the kth no de in very simple families of increasing trees (which includes, among others, binary increasing trees, re...

Ngày tải lên: 08/08/2014, 12:22

... The interest of circulant graphs in graph theory and applications has grown during the last two decades. They appeared in coding theory, VLSI design, Ramsey theory and other areas. Recently there ... denote the number of common neighbor s of the vertices a and b. The following theorem is the main tool in describing properties of the automorphisms of unitary Cayley graphs:...

Ngày tải lên: 08/08/2014, 14:22

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

... Ω ∞ ). We consider the following cases: 1. Case n = 2. Assume that in a neighborhood of the coordinate origin, ∂Ω coincides with a rectilinear angle having measure β. Then the problem (2.22) ... satisfying η(x, T )=0. Denote by m ∗ the number of multi-indices which have order not exceeding m, μ 0 is the constant in (1.3). From Theorems 3.1, 3.2 in [5] and by using induction...

Ngày tải lên: 06/08/2014, 05:20

... (in probability) then either the parent distribution belongs to the domain of attraction of the normal law or it has slowly varying tails and one of the two tails completely dominates the other. The ... distribution by the empirical distribution of the data in the definition of the statistical function, and then resampling the data to obtain a Monte Carlo distribution...

Ngày tải lên: 06/08/2014, 05:20