Sharif Digital Repository

Let G be a non-abelian group and let Z ( G ) be the center of G. Associate a graph ΓG (called non-commuting graph of G) with G as follows: Take G Z ( G ) as the vertices of ΓG and join two distinct vertices x and y, whenever x y ≠ y x. We want to explore how the graph theoretical properties of ΓG can effect on the group theoretical properties of G. We conjecture that if G and H are two non-abelian finite groups such that ΓG ≅ ΓH, then | G | = | H |. Among other results we show that if G is a finite non-abelian nilpotent group and H is a group such that ΓG ≅ ΓH and | G | = | H |, then H is nilpotent. © 2006 Elsevier Inc. All rights reserved  

The unit graph corresponding to an associative ring R is the graph obtained by setting all the elements of R to be the vertices and defining distinct vertices x and y to be adjacent if and only if x + y is a unit of R. By a constructive method, we derive necessary and sufficient conditions for unit graphs to be Hamiltonian  

A graph is called weakly perfect if its chromatic number equals its clique number. In this note a new class of weakly perfect graphs is presented and an explicit formula for the chromatic number of such graphs is given  

A graph is called weakly perfect if its chromatic number equals its clique number. In this paper a new class of weakly perfect graphs arising from rings are presented and an explicit formula for the chromatic number of such graphs is given. Copyright  

A signed graph Γ is said to be determined by its spectrum if every signed graph with the same spectrum as Γ is switching isomorphic with Γ. Here it is proved that the path Pn, interpreted as a signed graph, is determined by its spectrum if and only if n≡0,1, or 2 (mod 4), unless n∈{8,13,14,17,29}, or n=3. © 2018 Elsevier Inc  

In this paper, we discuss some recent results on graphs attached to rings. In particular, we deal with comaximal graphs, unit graphs, and total graphs. We then define the notion of cototal graph and, using this graph, we characterize the rings which are additively generated by their zero divisors. Finally, we glance at graphs attached to other algebraic structures  

In this paper, we deal with zero-divisor graphs of posets. We prove that the diameter of such a graph is either 1, 2 or 3 while its girth is either 3, 4 or ∞. We also characterize zero-divisor graphs of posets in terms of their diameter and girth  

The gain graphs are essential generalizations of the signed graphs. They are indeed directed graphs whose edges are labeled by the elements of a group rather than just ±1. In this paper, we prove the existence of matroids arising from these graphs. Further, we study the structure of the obtained matroids as well as their relation with the generalized Hamming weights, the regularity of the ideal of circuits, and the codes. © 2023 Elsevier B.V  

A tree containing exactly two non-pendant vertices is called a doublestar. A double-star with degree sequence (k1 +1, k2 +1, 1, ⋯ , 1) is denoted by Sk1,k2 . We study the edge-decomposition of graphs into double-stars. It was proved that every double-star of size k decomposes every 2k-regular graph. In this paper, we extend this result by showing that every graph in which every vertex has degree 2k + 1 or 2k + 2 and containing a 2-factor is decomposed into Sk1,k2 and Sk1-1,k2 , for all positive integers k1 and k2 such that k1 + k2 = k  

In this paper we study the structure of some special bases for the null space of the incidence matrix of a graph. Recently it was shown that if G is a graph with no cut vertex, then G has a {-1, 0, 1}-basis. We generalize this result showing that the statement remains valid for every graph with no cut edge. For the null space of any bipartite graph, we construct a {-1, 0, 1}-basis. For any bipartite graph we obtain the support sizes of all elements in the null space of its incidence matrix. Among other things, we prove that for a graph G, there exists a {-1, 1}-vector for the null space of G if and only if the degree of any vertex of G is even and G has an even number of edges. © 2005... 

The distributed nature and complexity of computer networks and various services provided via them, makes the networks vulnerable to numerous attacks. The TCP/IP presumptions which are based on using this protocol to provide a simple, open communication infrastructure in an academic and collaborative environment, causes this protocol lack of built-in mechanisms for authentication, integrity and privacy. Even though in the last few years a more systematic approach to TCP/IP network security problem has been followed, a formal approach to this problem is lacking. In this paper, we propose using Description Logics as a formal model which could be used to analyze TCP/IP networks against attacks.... 

Controlled graphitization has become known as a practical method for improvement of wear resistance and machining properties in steels. In this paper, the effect of heat treatment on microstructure of CK45 steel has been investigated. Austenitising was carried out at 920 °C for 5 h. Besides, isothermal transformation was conducted at 750 °C in the time range of 1-20 h. In this work, full potential carbon resource was tried to be used around samples as a factor to prevent the burning of the limited carbon in steel and also to increase the percentage of sample surface carbon in order to improve wear capability and machining. The microstructure of the steel considerably changes by this heat... 

To synthesize a novel biopolymer-based superabsorbent hydrogel, 2-acrylamido-2-methylpropanesulfonic acid (AMPS) was grafted onto kappa-carrageenan (KC) backbones. The graft copolymerization reaction was carried out in a homogeneous medium and in the presence of ammonium persulfate (APS) as an initiator, N,N,N',N'-tetramethyl ethylenediamine (TMEDA) as an accelerator, and N,N'-methylene bisacrylamide (MBA) as a crosslinker. A proposed mechanism for KC-g-AMPS formation was suggested and the hydrogel structure was confirmed using FTIR spectroscopy. The affecting variables on swelling capacity, i.e., the initiator, the crosslinker, and the monomer concentration, as well as reaction temperature,... 

Synthesis of polyvinyl pyrrolidone (PVP) coated ultrasmall Gd2O3 nanoparticles (NPs) with enhanced T1-weighted signal intensity and r2/r1 ratio close to unity is performed by a microwave-assisted polyol process. PVP coated Gd2O3NPs with spherical shape and uniform size of 2.5 ± 0.5 nm have been synthesized below 5 min and structure and morphology confirmed by HRTEM, XRD and FTIR. The longitudinal (r1) and transversal relaxation (r2) of Gd2O3NPs is measured by a 3 T MRI scanner. The results showed considerable increasing of relaxivity for Gd2O3NPs in... 

This paper proposes a high performance voltage tracking and current sharing among parallel connected inverters by applying optimal control and minimizing the cost function. The control system forces the voltage of load to track the voltage reference, and the current of all inverters becomes equal. Therefore, both current sharing and voltage tracking are obtained. In addition, the smallest input energy and simplicity in control circuit are the other advantages of the suggested method. To show the performance of the proposed control scheme, the simulations with two-modular practical systems are performed and the results are provided. The results indicate that the control objectives are... 

An analytical model is proposed to study the effect of particle size on melting enthalpy and entropy of metallic nanoparticles (NPs). The Mott's and Regel's equations for melting entropy in the combination of core average coordination number (CAC) and surface average coordination number (SAC) of freestanding NPs are considered. Clusters of icosahedral (IC), body centered cubic (BCC), and body centered tetragonal (BCT) structure without any vacancies and defects are modeled. Using the variable coordination number made this model to be in good agreement with experimental and molecular dynamic (MD) results of different crystal structures. The model predicts melting entropy and enthalpy of... 

Adaptive Noise Cancellation (ANC) is a well-known technique for background noise reduction in automobile and vehicular environments. The noise fields in automobile and other vehicle interior obey the diffuse noise field model closely. On the other hand, the ANC does not provide sufficient noise reduction in the diffuse noise fields. In this paper, a new multistage post-filter is designed for ANC as a solution to diffuse noise conditions. The designed post-filter is a single channel Linear Prediction (LP) based speech enhancement system. The LP is performed by an adaptive lattice filter and attempts to extract speech components by using intermediate ANC signals. The post-filter has no... 

Modeling and analysis of information system vulnerabilities helps us to predict possible attacks to networks using the network configuration and vulnerabilities information. As a fact, exploiting most of vulnerabilities result in access rights alteration. In this paper, we propose a new vulnerability analysis method based on the Take-Grant protection model. We extend the initial Take-Grant model to address the notion of vulnerabilities and introduce the vulnerabilities rewriting rules to specify how the protection state of the system can be changed by exploiting vulnerabilities. Our analysis is based on a bounded polynomial algorithm, which generates the closure of the Take-Grant graph... 

In this paper, for the first time, we present a small signal circuit model of quantum dot laser considering two photon modes, i.e., ground and first excited states lasing. By using the presented model, effect of temperature variations on modulation response of quantum dot laser is investigated. Simulation results of modulation response are in agreement with the numerical and experimental results reported by other researchers