s‐Regular cubic graphs as coverings of the complete bipartite graph K3,3

A graph is s‐regular if its automorphism group acts freely and transitively on the set of s‐arcs. An infinite family of cubic 1‐regular graphs was constructed in [10], as cyclic coverings of the three‐dimensional Hypercube. In this paper, we classify the s‐regular cyclic coverings of the complete bipartite graph K_3,3 for each ≥ 1 whose fibre‐preserving automorphism subgroups act arc‐transitively. As a result, a new infinite family of cubic 1‐regular graphs is constructed. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 101–112, 2004     

Kautz图的限制边连通度

限制边连通度是对传统边连通度的推广 ,而且是计算机互连网络容错性的一个重要度量 .本文考虑两类重要的网络模型———Kautz有向图K(d ,n)和Kautz无向图UK(d ,n)的限制边连通度λ′,并得到如下结果 :除了λ′(K( 2 ,1) )不存在外 ,均有λ′(K(d ,n) ) =2d-2 ;当d≥ 3 ,n≥ 3时 ,4d-5≤λ′(UK(d ,n) ) ≤ 4d -4 .     

Acyclic edge coloring of subcubic graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and it is denoted by a^′(G). From a result of Burnstein it follows that all subcubic graphs are acyclically edge colorable using five colors. This result is tight since there are 3-regular graphs which require five colors. In this paper we prove that any non-regular connected graph of maximum degree 3 is acyclically edge colorable using at most four colors. This result is tight since all edge maximal non-regular connected graphs of maximum degree 3 require four colors.     

Independent sets and 2‐factors in edge‐chromatic‐critical graphs

In 1968, Vizing made the following two conjectures for graphs which are critical with respect to the chromatic index: (1) every critical graph has a 2‐factor, and (2) every independent vertex set in a critical graph contains at most half of the vertices. We prove both conjectures for critical graphs with many edges, and determine upper bounds for the size of independent vertex sets in those graphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 113–118, 2004     

Data driven temperature dependence of EOS parameters

Using three kinds of experimental data (p_c, V_c and T_c at the critical state or P_s, V_s^v and V^sL at different temperatures for saturation data) three parameters of the EOS may be directly determined and the temperature dependence of the parameters may be established from thermodynamic conditions of vapour-liquid critical point or vapour-liquid phase equilibria respectively. The principle was demonstrated on the BACK EOS. Examples of argon and n-alkanes were used to demonstrate the idea. It was found, that there are two parameter sets of the BACK equation that satisfy the critical or saturation conditions for certain pure compounds. The BACK equation is able to reproduce experimental Z_c values for compounds above Z_c = 0.2764 (that is, for argon, methane, ethane), but it is improper for higher alkanes. In case of n-alkanes we found that there is no simple function for T dependence of BACK parameters. Parameter values obtained in the way demonstrated may be useful to give initial values for parameter estimation from experimental (e.g., VLE) data.     

Peculiarities of the vortex dynamics in YBa2Cu3Ox single crystals as revealed by irreversible microwave absorption

We report the results of a wide experimental study of the irreversible modulated microwave absorption as a function of temperature, applied magnetic field and modulation amplitude in the YBa₂Cu₃O_x single crystals. To analyze the experimental data the model of the microwave power dissipation by the flux lines has been developed taking into account thermal fluctuations, the distributions of currents and vortices over a sample. We have obtained the information about regimes of vortex motion in the different areas of the H–T phase diagram and estimated the values of flux flow viscosity and critical current density.     

On Cubic Graphs Admitting an Edge-Transitive Solvable Group

Using covering graph techniques, a structural result about connected cubic simple graphs admitting an edge-transitive solvable group of automorphisms is proved. This implies, among other, that every such graph can be obtained from either the 3-dipole Dip₃ or the complete graph K ₄, by a sequence of elementary-abelian covers. Another consequence of the main structural result is that the action of an arc-transitive solvable group on a connected cubic simple graph is at most 3-arc-transitive. As an application, a new infinite family of semisymmetric cubic graphs, arising as regular elementary abelian covering projections of K _3,3, is constructed.     

High-frequency oscillations,generated in the resistive state of a superconducting film

Summary The effect of non-Josephson generation (high-frequency oscillations of voltage) in the resistive state of the superconducting film is studied theoretically in the presence of a constant magnetic field. The density of the generation current in the magnetic field is calculated. The consideration is based on the earlier developed model, in which the above effect is due to the bremsstrahlung radiation from the particles with the energy ε>Δ which are injected from the quasi-normal layer of the phase slip centre to the superconducting bank. The quasi-particles pick up the energy in the process of the multiple Andreev scattering at theN-S boundaries, and the bremsstrahlung radiation is only possible if ε-Δ is of the order of the perturbation energy of the off-diagonal potential at theN-S boundary (~ΔΓ ^3/2, where γ is the depairing factor of the super-conductor).