Báo cáo toán học: "The spectral radius and the maximum degree of irregular graphs" doc

... spectral radius of a general (not necessarily regular) graph G and that of a subgraph of G, see [16]. 2 The spectral radius and the maximum degree The following theorem is the main result of this ... to the extreme entries of the principal eigenvector of an irregular graph G, then one can improve the result of Theorem 2.1. However, there are infini...

Ngày tải lên: 07/08/2014, 15:22

Ngày tải lên: 05/08/2014, 15:20

... Labels and Symmetry Numbers Let T be an element of C,andletv be a vertex of T . We define the symmetry label l T (v)ofv as follows: If v is the root of T ,thenl T (v)=1. Ifv is not the root of T, then ... largest in their equivalence class as standard trees, and use them as equivalence class representatives. We will de- note the set of standard Catalan trees by standard(C...

Ngày tải lên: 07/08/2014, 06:22

... statements of the theorem are implied by Theorem 1 and the following lemma. Lemma 1. If a is a member of the Catalan family then a = δa. Otherwise, a<δa. Proof. The proof is by induction on the generation ... direct proof of Theorem 3 and the reason is that there is an important difference in the distribution of labels in the Catalan family tree and the tree...

Ngày tải lên: 07/08/2014, 07:21

... each, and other random variables. Equiprobable allocations are the most simple and well studied. Consider, for example, an Internet voting on the theme: “Which of the N teams will win the world ... words with the same hash value. The model of random equiprobable allocations of particles (hash values of different input words) into N cells (elements of B) is often used...

Ngày tải lên: 07/08/2014, 07:21

... 1, in the expansion of κ(ω). To distinguish the steps of the original path from the steps of the inserted paths we will colour the former red and the latter blue. This leads to the idea of bi-coloured Dyck ... partition the path into y + 1 subpaths. The first of these is the Dyck path β 0 and the others are of the form u α β α , α =1, y,whereu α is a t...

Ngày tải lên: 07/08/2014, 08:20

... remove the edges of all white a i and black b i vertices on one side of , and the edges of all black a i and white b i vertices on the other side of .LetG + be the subgraph on one side of ,andG − the ... n)=2 n−m (2k  m;n +1) 2 . Proof. The proof is analogous to the proof of the previous corollary, and once again the odd factor 2k  m;n + 1 is the n...

Ngày tải lên: 07/08/2014, 08:22

... − e) , then µ (G) − µ (H) > 1 Diam (H) |H| . This lemma follows easily from Theorem 2.1 of [2] and its proof is omitted. Proofs Proof of Theorem 2 Write dist F (s, t) for the length of a shortest ... Mathematics, 184, Springer- Verlag, New York (1998), xiv+394 pp. [2] S. M. Cioab˘a, The spectral radius and the maximum degree of irregular graphs, Elec- tronic J....

Ngày tải lên: 07/08/2014, 13:21

... [11], and then prove this theorem. Sections 4 and 5 are devoted to the applications of Theorem 3.1 to geometric lattices and face posets of shellable complexes, respectively. Taken together, these ... (along with those of Chari and Swartz) give us the following. Theorem 1.1. Let ∆ be the order complex of a rank-selected subposet of either 1: a geometric lattice, or 2:...

Ngày tải lên: 08/08/2014, 12:23

... number of order n, i.e. the number of partitions of a set of n elements. In this paper we study the central moments of the Poisson distribution, and we show that they can be expressed using the ... the number of partitions of a set into subsets of size at least 2. 1 Introduction The moments of the Poisson distribution are well-known to be connected to the c...

Ngày tải lên: 08/08/2014, 14:22