Báo cáo toán học: "Revisiting two classical results on graph spectra" pps

... adjacency matrix of a graph G. The aim of this note is to refine quantitatively two well-known results on graph spectra. The first one, following from Frobenius’s theorem on nonnegative matrices, ... asserts that if H is a proper subgraph of a connected graph G, then µ (G) > µ (H) . The second one, due to H. Sachs [7], asserts that if G is a connected nonbipartite graph, then...

Ngày tải lên: 07/08/2014, 15:22

... analogous conditions for other elements of the group and to certain subgroups. In Section 2 we recall some notation along with the basic construction of the Leech lattice and the group ·0. In Section ... B belong to the same sextet. We extend this to a much less obvious necessary and sufficient condition, namely ζ A and ζ B will commute if and only if A∪B is contained in a block of S. We go on...

Ngày tải lên: 08/08/2014, 11:20

... G 3 \{u} is not connected, it has then two components. One of the component is H 3 for an appropriate graph H. If H is a tree then Ind(H 3 ) is contractible by lemma 7, Ind(G 3 \ {u}) is contractible ... simplex on V (G). If we contract this simplex we get a homotopy equivalent CW complex. The suspension is the double cone over (Ind(G)) ∗ . A cone is contractible, so we might contract o...

Ngày tải lên: 08/08/2014, 01:20

... pentagon and hexagon two- graphs below, I mean the two- graphs obtained from the pentagon and hexagon graphs by this procedure. All this material can be found in Seidel [9]. Let (X, V ) be a two- graph. ... relation defined earlier on any two- graph. Thus, reduced 5,6-free two- graphs correspond to series-reduced trees. For 5-free two- graphs, the difficulty is in the other direction....

Ngày tải lên: 07/08/2014, 06:20

... Violations of the symplectic condition are determined by ignoring the subscripts of the symbols γ t . The only point that needs careful consideration is the handling of cancellation. A violation ... presentation of Sch¨utzenberger’s involution. (4) The local rules thus expanded have certain restricted symmetries, namely a 180 o rotation and reflection in one diagonal. The restriction derives ....

Ngày tải lên: 07/08/2014, 08:22

... various correlation properties which exist between the two- parameter chromatic symmetric function and its corresponding graph. Additionally, for the complete graph G of order n, its corresponding two parame- ter ... interesting connection between our two parameter chromatic symmetric function Y G (x; q, t) and the Macdonald polynomials Q λ . We motivate this connection via the follo...

Ngày tải lên: 07/08/2014, 15:22

... n]; secondly, the {M S } partition of M. 4.1 Additional notation 4.1.1 The {X, y, Z} partition of [1, n] Our first piece of additional notation is motivated by the usefulness of the partition (x 1 , ... distribution of ∆ for larger values of µ using computer-aided enumerations. We begin by introducing two additional pieces of notation that will be used in this section: firstly, the {X, y, Z}...

Ngày tải lên: 07/08/2014, 15:22

... based on honeycomb tes- sellation and the protocol based on it, hexagonal cell-based data dissemination (HexDD). HexDD is a geographical routing protocol based on this virtual in- frastructure concept, ... this infrastructure, which considers dynamic conditions of multiple sinks and sources. The architecture consists of ‘highways’ in a honeycomb tessellation, which are the three main di...

Ngày tải lên: 20/06/2014, 20:20

... babble noise conditions. The experi- mental results show that the VAD based on MP coeffi- cients outperforms the ones based on the DFT in all of the testing conditions, and it can be concluded that ... shows in Section 4. Section 5 concludes this study. 2 Signal atomic decomposition based on conjugate subspace MP In this section, we will briefly review the process of sig- nal decompos...

Ngày tải lên: 20/06/2014, 21:20