Sharif Digital Repository

In this paper, we show that every (3k−3)-edge-connected graph G, under a certain degree condition, can be edge-decomposed into k factors G1,…,Gk such that for each vertex v∈V(Gi), |dGi(v)−dG(v)/k|<1, where 1≤i≤k. As an application, we deduce that every 6-edge-connected graph G can be edge-decomposed into three factors G1, G2, and G3 such that for each vertex v∈V(Gi) with 1≤i≤3, |dGi(v)−dG(v)/3|<1, unless G has exactly one vertex z with dG(z)⁄≡30. Next, we show that every odd-(3k−2)-edge-connected graph G can be edge-decomposed into k factors G1,…,Gk such that for each vertex v∈V(Gi), dGi(v) and dG(v) have the same parity and |dGi(v)−dG(v)/k|<2, where k is an odd positive integer and 1≤i≤k.... 

We present a Vector Dark Matter (VDM) model that explains the 3.5 keV line recently observed in the XMM-Newton observatory data from galaxy clusters. In this model, dark matter is composed of two vector bosons, V and V', which couple to the photon through an effective generalized Chern-Simons coupling, gV. V' is slightly heavier than V with a mass splitting mV' - mV 3.5 keV. The decay of V' to V and a photon gives rise to the 3.5 keV line. The production of V and V' takes place in the early universe within the freeze-in framework through the effective gV coupling when mV' < T < Λ, Λ being the cut-off above which the effective gV coupling is not valid. We introduce a high energy model that... 

The inclusion ideal graph of a ring R, denoted by In(R), is a graph whose vertices are all non-trivial left ideals of R and two distinct left ideals I and J are adjacent if and only if I⊆J or J⊆I. In this paper, we show that In(R) is not connected if and only if R≅M2(D) or D1×D2, for some division rings, D, D1 and D2. Moreover, if R is connected, then diam(In(R))≤3. We prove that if In(R) is a tree, then In(R) is a star graph or P4. Also, In(R) is a complete graph if and only if R is a uniserial ring. Next, it is shown that the inclusion ideal graph of Mn(D) for a division ring D and a natural number n>3 is not regular  

Introduction: Interindividual variations in regional structural properties covary across the brain, thus forming networks that change as a result of aging and accompanying neurological conditions. The alterations of superficial white matter (SWM) in Alzheimer's disease (AD) are of special interest, since they follow the AD-specific pattern characterized by the strongest neurodegeneration of the medial temporal lobe and association cortices. Methods: Here, we present an SWM network analysis in comparison with SWM topography based on the myelin content quantified with magnetization transfer ratio (MTR) for 39 areas in each hemisphere in 15 AD patients and 15 controls. The networks are... 

This paper presents the results of parametric analyses of the yielding moment (My) of Bolted Flush Endplate Beam (BFEB) splice connections using Finite Element Modeling (FEM) tools. The connection components were modeled using three-dimensional brick elements, while contact between the endplates was modeled using Coulomb friction. Materials for beam, endplate and bolts were considered to behave non-linearly. Finite element results with three experimental and numerical studies were compared, and all indicated good agreement, which is also briefly reviewed in this paper. Using verified FEM, fairly large parametric studies, based on the practical configuration of BFEB connections, were carried... 

The modified eccentricity connectivity polynomial of a connected graph G is defined as Ξ(G; x)=Σ u∈V(G)d G(u)x ε′G (u), where ε′ G(u)=Σ v∈NG(u)εG(u)and d G(u) is the degree of u in G. In this paper modified eccentric connectivity polynomial is computed for several classes of composite graphs  

Let γs′ (G) be the signed edge domination number of G. In 2006, Xu conjectured that: for any 2-connected graph G of order n (n ≥ 2), γs′ (G) ≥ 1. In this article we show that this conjecture is not true. More precisely, we show that for any positive integer m, there exists an m-connected graph G such that γs′ (G) ≤ - frac(m, 6) | V (G) |. Also for every two natural numbers m and n, we determine γs′ (Km, n), where Km, n is the complete bipartite graph with part sizes m and n. © 2008 Elsevier B.V. All rights reserved  

Purpose: Alzheimer's disease (AD) starts years before its signs and symptoms including the dementia become apparent. Diagnosis of the AD in the early stages is important to reduce the speed of brain decline. Aim of the study: Identifying the alterations in the functional connectivity of the brain during the disease stages is among the main important issues in this regard. Therefore, in this study, the changes in the functional connectivity during the AD stages were analyzed. Materials and methods: By employing the functional magnetic resonance imaging (fMRI) data and graph theory, weighted undirected graphs of the whole-brain and default mode network (DMN) network were investigated... 

A new semi-rigid beam-to-column, as well as bracing-to-frame, connection has been developed. In addition to its application in building structures, due to its special features and characteristics, it can best lend itself to offshore jackets, where fracture caused by fatigue has always been a major concern. The adverse effects of welding, material embrittlement, residual stresses, etc., pronounced by cyclic loading on such structures, can be overcome by using this new connection. Moreover, it can be easily used in the structure of various modules used in the topside of platforms and FPSOs. The particular feature of this connection is its geometry, which is so devised that it allows much... 

This paper introduces a parallel algorithm for computing an N = n2n point Lagrange interpolation on an n-dimensional cube-connected cycles (CCCn). The algorithm consists of three phases: initialisation, main and final. While there is no computation in the initialisation phase, the main phase is composed of n2n-1 steps, each consisting of four multiplications, four subtractions and one communication operation, and an additional step including one division and one multiplication. The final phase is carried out in two sub-phases. There are [n/2] steps in the first sub-phase, each including two additions and one communication, followed by the second sub-phase which comprises n steps each... 

Let G be a graph and let f be a positive integer-valued function on V(G). In this paper, we show that if for all S⊆V(G), ω(G∖S)<∑v∈S(f(v)−2)+2+ω(G[S]), then G has a spanning tree T containing an arbitrary given matching such that for each vertex v, dT(v)≤f(v), where ω(G∖S) denotes the number of components of G∖S and ω(G[S]) denotes the number of components of the induced subgraph G[S] with the vertex set S. This is an improvement of several results. Next, we prove that if for all S⊆V(G), ω(G∖S)≤∑v∈S(f(v)−1)+1, then G admits a spanning closed walk passing through the edges of an arbitrary given matching meeting each vertex v at most f(v) times. This result solves a long-standing conjecture... 

In this paper we define critical graphs as minimal graphs that support a given set of rates for the index coding problem, and study them for both the one-shot and asymptotic setups. For the case of equal rates, we find the critical graph with minimum number of edges for both one-shot and asymptotic cases. For the general case of possibly distinct rates, we show that for one-shot and asymptotic linear index coding, as well as asymptotic non-linear index coding, each critical graph is a union of disjoint strongly connected subgraphs (USCS). On the other hand, we identify a non-USCS critical graph for a one-shot non-linear index coding problem. In addition, we show that the capacity region of... 

Security techniques have been designed to obtain certain objectives. One of the most important objectives all security mechanisms try to achieve is the availability, which insures that network services are available to various entities in the network when required. But there has not been any certain parameter to measure this objective in network. In this paper we consider availability as a security parameter in ad-hoc networks. However this parameter can be used in other networks as well. We also present the connectivity coefficient of nodes in a network which shows how important is a node in a network and how much damage is caused if a certain node is compromised