Sharif Digital Repository

Let G be a simple graph of order n. We mean by dominating set, a set S C V(G) such that every vertex of G is either in S or adjacent to a vertex in S. The domination polynomial of G is the polynomial Σni=1 (G,i)xi where d((g,i) is the number of dominating sets of G of size i. Two graphs G and H are said to be V-equivalent, written G H, if D((G, x) = D(H, x). The D-equivalence class of G is [G] = { H H G }. Recently, the determination of D-equivalence class of a given graph, has been of interest. In this paper, it is shown that for n ≥ 3, [Kn, n] has size two. We conjecture that the complete bipartite graph Km,n for n - m ≥ 2, is uniquely determined by its domination polynomial  

Let R be a commutative ring with unity and R+, U(R), and Z*(R) be the additive group, the set of unit elements, and the set of all nonzero zero-divisors of R, respectively. We denote by ℂAY(R) and GR, the Cayley graph Cay(R+, Z*(R)) and the unitary Cayley graph Cay(R+, U(R)), respectively. For an Artinian ring R, Akhtar et al. (2009) studied GR. In this article, we study ℂAY(R) and determine the clique number, chromatic number, edge chromatic number, domination number, and the girth of ℂAY(R). We also characterize all rings R whose ℂAY(R) is planar. Moreover, we determine all finite rings R whose ℂAY(R) is strongly regular. We prove that ℂAY(R) is strongly regular if and only if it is edge... 

When a transparent plane-parallel plate is illuminated at a boundary region by a parallel monochromatic beam of light, Fresnel diffraction occurs because of the abrupt change in phase imposed by the finite change in refractive index at the plate boundary. The intensity of the diffraction fringes varies periodically with changes in the optical path difference of the light passing through the plate edge. The optical path difference depends on the incident angle of the light, the refractive index of the plate and surrounding medium, and the wavelength of the light. Plotting the intensity of the diffraction fringes versus optical path difference provides a general phase shift method for phase... 

Let R be a commutative ring with unity and R+ and Z*(R) be the additive group and the set of all nonzero zero-divisors of R, respectively. We denote by ℂ𝔸𝕐(R) the Cayley graph Cay(R+, Z*(R)). In this article, we study ℂ𝔸𝕐(R). Among other results, it is shown that for every zero-dimensional nonlocal ring R, ℂ𝔸𝕐(R) is a connected graph of diameter 2. Moreover, for a finite ring R, we obtain the vertex connectivity and the edge connectivity of ℂ𝔸𝕐(R). As a result, ℂ𝔸𝕐(R) gives an algebraic construction for vertex transitive graphs of maximum connectivity. In addition, we characterize all zero-dimensional semilocal... 

It is well known that all starlike trees, i.e. trees with exactly one vertex of degree at least three, are determined by their Laplacian spectrum. A double starlike tree is a tree with exactly two vertices of degree at least three. In 2009, the following question was posed: Are all the double starlike trees determined by their Laplacian spectra? In this direction, it was proved that one special double starlike tree Hn(p,p) is determined by its Laplacian spectrum, where Hn(p,q) is a tree obtained by joining p pendant vertices to an end vertex of a path of order and then joining pendant vertices to another end of the path. Also, the banana tree Bn,k is a tree obtained by joining a vertex to... 

Objectives: This study aimed to investigate the effect of upper extremity coordination exercises based on fatigue prediction on fine and gross manual dexterity, upper limb motor function, shoulder and elbow proprioception, occupational performance, and activities of daily living in chronic stroke survivors. Methods: In this pilot double-blind randomized clinical trial, 24 chronic strokes were enrolled using the non-probability sampling method. Participants were randomly allocated to the control (received routine occupational therapy) and intervention (received upper extremity coordination exercises based on fatigue prediction using the Kinect) groups. Before and after the interventions (six... 

In this brief, an open-loop double-carrier simultaneous wireless power and data transfer system is presented. Although the system is intended for implantable biomedical microsystems, it can also be used for other low-power applications such as Internet of Things (IoT). In the proposed system, uplink data communication (from the implant to the outside of the body) is implemented by switching a capacitor on the implant site. This switching results in changing the resonance frequency between two different frequencies during different periods of time. To keep the power transfer efficiency (PTE) and the power delivered to the load (PDL) almost constant, two external power transmitters, each... 

Let R be a commutative ring with identity, and let A(R) be the set of ideals with non-zero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)* = A(R) {0}, and two distinct vertices I and J are adjacent if and only if IJ = 0. In this paper, we study some connections between the graph theoretic properties of this graph and some algebraic properties of a commutative ring. We prove that if AG(R) is a tree, then either AG(R) is a star graph or a path of order 4 and, in the latter case, R = F × S, where F is a field and S is a ring with a unique non-trivial ideal. Moreover, we prove that if R has at least three minimal prime ideals, then AG(R) is... 

Suppose that R is a commutative ring with identity. Let A(R) be the set of all ideals of R with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A( R)*=A(R)(0) and two distinct vertices I and J are adjacent if and only if IJ=(0). In Behboodi and Rakeei (2011) [8], it was conjectured that for a reduced ring R with more than two minimal prime ideals, girth(AG(R))=3. Here, we prove that for every (not necessarily reduced) ring R, ω(AG(R))<|Min(R)|, which shows that the conjecture is true. Also in this paper, we present some results on the clique number and the chromatic number of the annihilating-ideal graph of a commutative ring. Among... 

In this research, a modified, cost effective sol-gel procedure applied to synthesize BaTiO3 nanoparticles. XRD and electron microscopy (SEM and TEM) applied for microstructural characterization of powders. The obtained results showed that the type of precursors, their ratio and the hydrolysis conditions had a great effect on time, temperature and therefore the costs of the synthesis process. By selection, utilization of optimized precursor's type, hydrolysis conditions, fine cubic BaTiO3 nanoparticles were synthesized at low temperature and in short time span (1 h calcination at 800 °C). The proposed procedure seems to be more preferable for mass production. The result indicated that the... 

Let G be a group. The power graph of G is a graph with the vertex set G, having an edge between two elements whenever one is a power of the other. We characterize nilpotent groups whose power graphs have finite independence number. For a bounded exponent group, we prove its power graph is a perfect graph and we determine its clique/chromatic number. Furthermore, it is proved that for every group G, the clique number of the power graph of G is at most countably infinite. We also measure how close the power graph is to the commuting graph by introducing a new graph which lies in between. We call this new graph the enhanced power graph. For an arbitrary pair of these three graphs we... 

Sensors are among essential building blocks of any Cyber-Physical Systems (CPSs). Acquisition and processing of their sensory data contribute to the power consumption and computation load of the overall CPSs. For data acquisition, the conventional fixed frequency sampling in many such systems is sub-optimal since a sizable number of samples do not contain important information. In this work, we propose a Signal-Dependent Sampling (SDS) method and present its associated circuit implementation. Using the proposed SDS method, the number of retained samples is significantly reduced with little or negligible compromise in the quality of the (reconstructed) signal. The associated error and added... 

Given the emergence of the Internet of Things (IoT) Cyber-Physical Systems (CPSs) and their omnipresence, reducing their power consumption is among the major design priorities. To reduce the power consumption of such systems, we propose the use of a signal-dependent sampling method in a bottom-up fashion, which can lead to up to a 94% reduction in the overall system power with negligible or no loss in performance. Moreover, the proposed technique provides further flexibility for self-aware CPSs to dynamically adjust the number of data samples that are needed for processing (and consequently reduce the power consumption) based on the application at hand and the desired trade-off between... 

Inclusion of nano-clays into hydrogels is an efficient approach to produce nanocomposite hydrogels. The introduction of nano-clay into hydrogels causes an increase in water absorbency. In the present work, Nanocomposite hydro-gels based on kappa-carrageenan were synthesized using sodium montmorillonite as nano-clay. Acrylamide and meth-ylenebisacrylamide were used as monomer and crosslinker, respectively. The structure of nanocomposite hydrogels was investigated by XRD and SEM techniques. Swelling behavior of nanocomposite hydrogels was studied by varying clay and carrageenan contents as well as methylenebisacrylamide concentration. An optimum swelling capacity was achieved at 12% of sodium...