Sharif Digital Repository

The energy ϵ(G) of a graph G is the sum of the absolute values of all eigenvalues of G. Zhou in (MATCH Commun. Math. Comput. Chem. 55 (2006) 91-94) studied the problem of bounding the graph energy in terms of the minimum degree together with other parameters. He proved his result for quadrangle-free graphs. Recently, in (MATCH Commun. Math. Comput. Chem. 81 (2019) 393-404) it is shown that for every graph G, ϵ(G) ≥ 2δ(G), where δ(G) is the minimum degree of G, and the equality holds if and only if G is a complete multipartite graph with equal size of parts. Here, we provide a short proof for this result. Also, we give an affirmative answer to a problem proposed in (MATCH Commun. Math.... 

A mixed graph is obtained from a graph by orienting some of its edges. The Hermitian adjacency matrix of a mixed graph with the vertex set {v1,…,vn}, is the matrix H=[hij]n×n, where hij=−hji=i if there is a directed edge from vi to vj, hij=1 if there exists an undirected edge between vi and vj, and hij=0 otherwise. The Hermitian spectrum of a mixed graph is defined to be the spectrum of its Hermitian adjacency matrix. In this paper we study mixed graphs which are determined by their Hermitian spectrum (DHS). First, we show that each mixed cycle is switching equivalent to either a mixed cycle with no directed edges (Cn), a mixed cycle with exactly one directed edge (Cn 1), or a mixed cycle... 

The energy of a graph G, E(G), is defined as the sum of absolute values of the eigenvalues of its adjacency matrix. In Akbari and Hosseinzadeh (2020) [3] it was conjectured that for every graph G with maximum degree Δ(G) and minimum degree δ(G) whose adjacency matrix is non-singular, E(G)≥Δ(G)+δ(G) and the equality holds if and only if G is a complete graph. Let G be a connected graph with the edge set E(G). In this paper, first we show that E(L(G))≥|E(G)|+Δ(G)−5, where L(G) denotes the line graph of G. Next, using this result, we prove the validity of the conjecture for the line of each connected graph of order at least 7. © 2021 Elsevier Inc  

This study introduces two new, simple, and scalable methods for synthesis of “cysteine–graphene oxide” hybrid, namely nucleophilic and covalent methods. Produced adsorbents could uptake 500 and 600 mg Hg2+/g, respectively, which are larger than capacities of most of the commercial adsorbents. By means of different instrumental techniques, chemical structures of the obtained graphene products were disclosed, and two pertinent mechanisms for their formations were suggested. Time for attaining uptake equilibrium for nucleophilic/covalent samples was 30 min/150 min, and kinetics was controlled by liquid film resistance/chemical reaction mechanisms, respectively. High selectivity and good... 

Recently, an approximate boundary condition [Opt. Lett. 38, 3009 (2013)] was proposed for fast analysis of onedimensional periodic arrays of graphene ribbons by using the Fourier modal method (FMM). Correct factorization rules are applicable to this approximate boundary condition where graphene is modeled as surface conductivity. We extend this approach to obtain the optical properties of two-dimensional periodic arrays of graphene. In this work, optical absorption of graphene squares in a checkerboard pattern and graphene nanodisks in a hexagonal lattice are calculated by the proposed formalism. The achieved results are compared with the conventional FMM, in which graphene is modeled as a... 

Recently, an approximate formalism [Opt. Express 23, 2764, (2015)] called diffractive interface theory has been reported for the fast analysis of the optical response of metasurfaces, subwavelength two-dimensional periodic arrays. In this method, the electromagnetic boundary conditions are derived using the susceptibility distribution of the metasurface, such that the analysis of metasurface is possible without solving any eigenvalue equation inside the grating layer. In this paper, we modify the boundary conditions to achieve more accurate results. In addition, in this paper, correct Fourier factorization rules are also applied leading to faster convergence rate. The obtained results are... 

Let G be a graph. An edge orientation of G is called smooth if the in-degree and the out-degree of every vertex differ by at most one. In this paper, we show that if G is a 2-edge-connected non-bipartite graph with δ(G)≥3, then G has a smooth primitive orientation. Among other results, using the spectral radius of digraphs, we show that if D1 is a primitive regular orientation and D2 is a non-regular orientation of a given graph, then for sufficiently large t, the number of closed walks of length t in D1 is more than the number of closed walks of length t in D2. © 2016 Elsevier Inc  

The singular values of a matrix A are defined as the square roots of the eigenvalues of A⁎A, and the energy of A denoted by E(A) is the sum of its singular values. The energy of a graph G, E(G), is defined as the sum of absolute values of the eigenvalues of its adjacency matrix. In this paper, we prove that if A is a Hermitian matrix with the block form A=(BDD⁎C), then E(A)≥2E(D). Also, we show that if G is a graph and H is a spanning subgraph of G such that E(H) is an edge cut of G, then E(H)≤E(G), i.e., adding any number of edges to each part of a bipartite graph does not decrease its energy. Let G be a connected graph of order n and size m with the adjacency matrix A. It is well-known... 

A circular zero-sum flow for a graph G is a function f: E(G) → R { 0 } such that for every vertex v, ∑e∈Evf(e)=0, where Ev is the set of all edges incident with v. If for each edge e, 1 ≤ | f(e) | ≤ r- 1 , where r≥ 2 is a real number, then f is called a circular zero-sum r-flow. Also, if r is a positive integer and for each edge e, f(e) is an integer, then f is called a zero-sum r-flow. If G has a circular zero-sum flow, then the minimum r≥ 2 for which G has a circular zero-sum r-flow is called the circular zero-sum flow number of G and is denoted by Φ c(G). Also, the minimum integer r≥ 2 for which G has a zero-sum r-flow is called the flow number for G and is denoted by Φ (G). In this... 

Cross-docking is a new logistic technique that brings considerable benefits such as low inventory level, customer satisfaction, etc. To achieve these benefits, coordination between transportation facilities is quite important. This paper studies both inbound and outbound scheduling problem and assignment of products from inbound truck to outbound trucks in a cross-docking warehouse including multiple receiving and shipping dock doors. To do so, an MILP model is developed, which is NP-hard. Thus, a GA algorithm is developed and has been strengthened with two proposed neighborhood search to tackle the developed problem in medium and large size instances. Finally, numerical results of three... 

Centrifugal microfluidics or the Lab on a CD (LOCD) has developed vast applications in biomedical researches and analyses. Fluid mixing is an application of the LOCD. In this paper, multiple centrifugal micromixers were simulated. Various parameters were originally presumed to have an effect on mixing performance. These parameters include inlet angle, angular velocity, cross-sectional profile, perpendicular length ratio and the number of channels in series. They were each analyzed through simulations. It was gathered that the inlet angle does not significantly affect the mixing quality. Increasing angular velocity steadily increases mixing quality for all geometries. The vertical triangular... 

The energy of a graph G, ϵ(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. The matching number µ(G) is the number of edges in a maximum matching. In this paper, for a connected graph G of order n with largest vertex degree ∆ ≥ 6 we present two new upper bounds for the energy of a graph: (Formula presented) and (Formula presented). The latter one improves recently obtained bound (Formula presented) where ∆e stands for the largest edge degree and a = 2(∆e + 1). We also present a short proof of this result and several open problems. © 2021  

The energy of a graph G, ϵ(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. The matching number µ(G) is the number of edges in a maximum matching. In this paper, for a connected graph G of order n with largest vertex degree ∆ ≥ 6 we present two new upper bounds for the energy of a graph: (Formula presented) and (Formula presented). The latter one improves recently obtained bound (Formula presented) where ∆e stands for the largest edge degree and a = 2(∆e + 1). We also present a short proof of this result and several open problems. © 2021  

Let R be a non-commutative ring. The commuting graph of R denoted by Λ (R), is a graph with vertex set R Z(R), and two distinct vertices a and b are adjacent if ab = ba. In this paper we investigate some properties of Λ(R), whenever R is a finite semisimple ring. For any finite field F, we obtain minimum degree, maximum degree and clique number of Λ(M n (F)). Also it is shown that for any two finite semisimple rings R and S, if Λ(R) ≃ Λ(S), then there are commutative semisimple rings R1 and S1 and semisimple ring T such that R ≃T × R1, S ≃ T × S1 and |R1| = |S1|. © 2004 Elsevier Inc. All rights reserved  

Let G be a graph with the vertex set {v1,…,vn}. The Seidel matrix of G is an [Formula presented] matrix whose diagonal entries are zero, ij-th entry is −1 if vi and vj are adjacent and otherwise is 1. The Seidel energy of G, denoted by [Formula presented], is defined to be the sum of absolute values of all eigenvalues of the Seidel matrix of G. Haemers conjectured that the Seidel energy of any graph of order n is at least [Formula presented] and, up to Seidel equivalence, the equality holds for Kn. Recently, this conjecture was proved for [Formula presented]. We establish the validity of Haemers’ Conjecture in general. © 2020 Elsevier Ltd  

A graph is called equimatchable if all of its maximal matchings have the same size. Kawarabayashi, Plummer, and Saito showed that the only connected equimatchable 3-regular graphs are K4 and K3, 3. We extend this result by showing that for an odd positive integer r, if G is a connected equimatchable r-regular graph, then G ϵ {Kr+1, Kr,r}. Also it is proved that for an even r, a connected triangle-free equimatchable r-regular graph is isomorphic to one of the graphs C5, C7, and Kr,r. © 2017 Wiley Periodicals, Inc  

(Chemical Equation Presented) New 2-aryl-4-chloro-3-hydroxy-1H-indole-5,7- dicarbaldehydes were synthesized in three steps from acetophenone derivatives. By oxidation of acetophenones to aryl glyoxals using selenium dioxide and condensation with acetylacetone in the presence of ammonium acetate in water 3-acetyl-5-aryl-4-hydroxy-2-methyl-1H-pyrrols were obtained. 2-Aryl-4-chloro-3-hydroxy-1H-indole-5,7-dicarbaldehydes were synthesized via Vilsmeier-Haack reaction of pyrrole derivatives in moderate yields  

Let G be a simple graph of order n and size m which is not a tree. If ℓ; ≤ 3 is a natural number and the length of every cycle of G is divisible by ℓ, then m ≤l/l-2 (n -2), and the equality holds if and only if the following hold: (i) ℓ is odd and G is a cycle of order ℓ or (ii) ℓ is even and G is a generalized 6>-graph with paths of length |l/2 It is shown that for a (0 mod ℓ)-cycle graph, m/n < l/l-1 if ℓ is odd, and for a given e > 0, there exists a (0 mod ℓ)-cycle graph G with m/n > l/l-2 - e. Also m/n > l/l-2 if ℓ is even, and for a given e > 0, there exists a (0 mod ℓ)-cycle graph G with m/n l/l-2-e  

We develop an integrated vendor-buyer model for a two-stage supply chain. The vendor manufactures the product and delivers it in a number of equal-sized batches to the buyer. The items delivered are presented to the end customers in a display area. Demand is assumed to be positively dependent on the amount of items displayed. The objective is to maximize total supply chain profit. The numerical analysis shows that buyer-vendor coordination is more profitable in situations when demand is more stock dependent. It also shows that the effect of double marginalization provides a link between the non-coordinated and the coordinated case  

In this paper, we introduce limited-sharing multiparty computation; in which there is a network of workers (processors) and a set of sources, each having access to a massive matrix as a private input. These sources aim to offload the task of computing a polynomial function of the matrices to the workers, while preserving the privacy of data. We also assume that the load of the link between each source and each worker is upper bounded by a fraction of each input matrix for some cin{1, rac{1}{2},rac{1}{3}, ldots}. The objective is to minimize the number of workers needed to perform the computation, such that even if an arbitrary subset of t-1 workers, for some tin mathbb{N}, collude, they...