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On the minimum energy of regular graphs
, Article Linear Algebra and Its Applications ; Volume 581 , 2019 , Pages 51-71 ; 00243795 (ISSN) ; Akbari, S ; Ghasemian, E ; Ghodrati, A. H ; Hosseinzadeh, M. A ; Koorepazan Moftakhar, F ; Sharif University of Technology
Elsevier Inc
2019
Abstract
The energy of a graph G, E(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. Gutman et al. proved that for every cubic graph of order n, E(G)≥n. Here, we improve this result by showing that if G is a connected subcubic graph of order n≥8, then E(G)≥1.01n. Also, we prove that if G is a traceable subcubic graph of order n≥8, then E(G)>1.1n. Let G be a connected cubic graph of order n≥8, it is shown that E(G)>n+2. It was proved that if G is a connected cubic graph of order n, then E(G)≤1.65n. Also, in this paper we would like to present the best lower bound for the energy of a connected cubic graph. We introduce an infinite family of connected cubic graphs whose for...
Color PCA eigenimages and their application to compression and watermarking
, Article Image and Vision Computing ; Volume 26, Issue 7 , 2008 , Pages 878-890 ; 02628856 (ISSN) ; Kasaei, S ; Sharif University of Technology
Elsevier Ltd
2008
Abstract
From the birth of multi-spectral imaging techniques, there has been a tendency to consider and process this new type of data as a set of parallel gray-scale images, instead of an ensemble of an n-D realization. However, it has been proved that using vector-based tools leads to a more appropriate understanding of color images and thus more efficient algorithms for processing them. Such tools are able to take into consideration the high correlation of the color components and thus to successfully carry out energy compaction. In this paper, a novel method is proposed to utilize the principal component analysis in the neighborhoods of an image in order to extract the corresponding eigenimages....
Collective dynamics of interacting particles in unsteady flows
, Article SIAM Journal on Applied Dynamical Systems ; Vol. 13, Issue. 1 , 2014 , pp. 194-209 ; ISSN: 15360040 ; Jalali, M. A ; Sharif University of Technology
Abstract
We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a longrange attractive and a short-range repulsive potential field known as Morse potential. We assume Stokesian drag force between particles and their carrier fluid and find analytic single-peaked traveling solutions for the spatial density of particles in the catastrophic phase. In steady flow conditions the streaming velocity of particles is identical to their carrier fluid, but we show that particle streaming is asynchronous with an unsteady carrier fluid. Using linear perturbation analysis, the stability...
NLOS identification in range-based source localization: statistical approach
, Article IEEE Sensors Journal ; Volume 18, Issue 9 , 1 May , 2018 , Pages 3745-3751 ; 1530437X (ISSN) ; Behnia, F ; Amiri, R ; Marvasti, F ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2018
Abstract
Least squares estimation is a widely-used technique for range-based source localization, which obtains the most probable position of mobile station. These methods cannot provide desirable accuracy in the case with a non line of sight (NLOS) path between mobile station and base stations. To circumvent this drawback, many algorithms have been proposed to identify and mitigate this error; however, they have a large run-time overhead. On the other hand, new positioning systems utilize a large set of base stations, and a practical algorithm should be fast enough to deal with them. In this paper, we propose a novel algorithm based on subspace method to identify and eliminate the NLOS error....
A new simplified formula in prediction of the resonance velocity for multiple masses traversing a thin beam
, Article Scientia Iranica ; Volume 23, Issue 1 , 2016 , Pages 133-141 ; 10263098 (ISSN) ; Mofid, M ; Eftekhar Azam, S ; Ebrahimzadeh Hassanabadi, M ; Sharif University of Technology
Abstract
In this article, transverse vibration of an Euler-Bernoulli beam carrying a series of traveling masses is analyzed. A semi-analytical approach based on eigenfunction expansion method is employed to achieve the dynamic response of the beam. The inertia of the traveling masses changes the fundamental period of the base beam. Therefore, a comprehensive parametric survey is required to reveal the resonance velocity of the traversing inertial loads. In order to facilitate resonance detection for engineering practitioners, a new simplified formula is proposed to approximate the resonance velocity
The algebraic connectivity of a graph and its complement
, Article Linear Algebra and Its Applications ; Volume 555 , 2018 , Pages 157-162 ; 00243795 (ISSN) ; Akbari, S ; Moghaddamzadeh, M. J ; Mohar, B ; Sharif University of Technology
Elsevier Inc
2018
Abstract
For a graph G, let λ2(G) denote its second smallest Laplacian eigenvalue. It was conjectured that λ2(G)+λ2(G‾)≥1, where G‾ is the complement of G. In this paper, it is shown that max{λ2(G),λ2(G‾)}≥[Formula presented]. © 2018 Elsevier Inc
Some results on the Laplacian spread conjecture
, Article Linear Algebra and Its Applications ; Volume 574 , 2019 , Pages 22-29 ; 00243795 (ISSN) ; Akbari, S ; Sharif University of Technology
Elsevier Inc
2019
Abstract
For a graph G of order n, let λ 2 (G) denote its second smallest Laplacian eigenvalue. It was conjectured that λ 2 (G)+λ 2 (G‾)≥1, where G‾ is the complement of G. For any x∈R n , let ∇ x ∈R (n2) be the vector whose {i,j}-th entry is |x i −x j |. In this paper, we show the aforementioned conjecture is equivalent to prove that every two orthonormal vectors f,g∈R n with zero mean satisfy ‖∇ f −∇ g ‖ 2 ≥2. In this article, it is shown that for the validity of the conjecture it suffices to prove that the conjecture holds for all permutation graphs. © 2019 Elsevier Inc
A note on the algebraic connectivity of a graph and its complement
, Article Linear and Multilinear Algebra ; 2019 ; 03081087 (ISSN) ; Akbari, S ; Sharif University of Technology
Taylor and Francis Ltd
2019
Abstract
For a graph G, let λ2(G) denote its second smallest Laplacian eigenvalue. It was conjectured that (Formula presented.), where (Formula presented.) is the complement of G. In this paper, it is shown that (Formula presented.). © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group
A note on the algebraic connectivity of a graph and its complement
, Article Linear and Multilinear Algebra ; 2019 ; 03081087 (ISSN) ; Akbari, S
Taylor and Francis Ltd
2019
Abstract
For a graph G, let λ2(G) denote its second smallest Laplacian eigenvalue. It was conjectured that (Formula presented.), where (Formula presented.) is the complement of G. In this paper, it is shown that (Formula presented.). © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group
A note on the algebraic connectivity of a graph and its complement
, Article Linear and Multilinear Algebra ; Volume 69, Issue 7 , 2021 , Pages 1248-1254 ; 03081087 (ISSN) ; Akbari, S ; Sharif University of Technology
Taylor and Francis Ltd
2021
Abstract
For a graph G, let (Formula presented.) denote its second smallest Laplacian eigenvalue. It was conjectured that (Formula presented.), where (Formula presented.) is the complement of G. In this paper, it is shown that (Formula presented.). © 2019 Informa UK Limited, trading as Taylor & Francis Group
A note on the algebraic connectivity of a graph and its complement
, Article Linear and Multilinear Algebra ; Volume 69, Issue 7 , 2021 , Pages 1248-1254 ; 03081087 (ISSN) ; Akbari, S ; Sharif University of Technology
Taylor and Francis Ltd
2021
Abstract
For a graph G, let (Formula presented.) denote its second smallest Laplacian eigenvalue. It was conjectured that (Formula presented.), where (Formula presented.) is the complement of G. In this paper, it is shown that (Formula presented.). © 2019 Informa UK Limited, trading as Taylor & Francis Group
Laplacian eigenvalue distribution and graph parameters
, Article Linear Algebra and Its Applications ; Volume 632 , 2022 , Pages 1-14 ; 00243795 (ISSN) ; Akbari, S ; Fakharan, M. H ; Trevisan, V ; Sharif University of Technology
Elsevier Inc
2022
Abstract
Let G be a graph and I be an interval. In this paper, we present bounds for the number mGI of Laplacian eigenvalues in I in terms of structural parameters of G. In particular, we show that mG(n−α(G),n]≤n−α(G) and mG(n−d(G)+3,n]≤n−d(G)−1, where α(G) and d(G) denote the independence number and the diameter of G, respectively. Also, we characterize bipartite graphs that satisfy mG[0,1)=α(G). Further, in the case of triangle-free or quadrangle-free, we prove that mG(n−1,n]≤1. © 2021 Elsevier Inc
Gold at crossroads of radical generation and scavenging at density functional theory level: Nitrogen and oxygen free radicals versus their precursors in the face of nanogold
, Article Journal of Physical Organic Chemistry ; Volume 34, Issue 1 , 2021 ; 08943230 (ISSN) ; Kassaee, M. Z ; Ayoubi Chianeh, M ; Fattahi, A ; Sharif University of Technology
John Wiley and Sons Ltd
2021
Abstract
In our previous report (J. Phys. Org. Chem., 2017), we discussed the dual behavior of gold nanocluster (Au3 NC), where it scavenged reactive oxygen species (ROS) while promoted their generation to a lesser extent. Continuing this quest, we investigate the effects of Au3 NC on common reactive nitrogen species (RNS: O=N˙ and O=N-O) and their precursors (O=N-H and O=N-O-H, respectively), at B3LYP/LACVP+* level of theory. We compare the results with those of prevalent ROS (H-O˙ and H-O-O˙) and their precursors (H-O-H and H-O-O-H, respectively). To this end, various parameters are probed such as binding energy (Eb), bond dissociation energy (BDE), bond lengths, Mullikan spin density (MSD),...
Gold at crossroads of radical generation and scavenging at density functional theory level: Nitrogen and oxygen free radicals versus their precursors in the face of nanogold
, Article Journal of Physical Organic Chemistry ; Volume 34, Issue 1 , 2021 ; 08943230 (ISSN) ; Kassaee, M.Z ; Ayoubi-Chianeh, M ; Fattahi, A ; Sharif University of Technology
John Wiley and Sons Ltd
2021
Abstract
In our previous report (J. Phys. Org. Chem., 2017), we discussed the dual behavior of gold nanocluster (Au3 NC), where it scavenged reactive oxygen species (ROS) while promoted their generation to a lesser extent. Continuing this quest, we investigate the effects of Au3 NC on common reactive nitrogen species (RNS: O=N˙ and O=N-O) and their precursors (O=N-H and O=N-O-H, respectively), at B3LYP/LACVP+* level of theory. We compare the results with those of prevalent ROS (H-O˙ and H-O-O˙) and their precursors (H-O-H and H-O-O-H, respectively). To this end, various parameters are probed such as binding energy (Eb), bond dissociation energy (BDE), bond lengths, Mullikan spin density (MSD),...
A lower bound for algebraic connectivity based on the connection-graph- stability method
, Article Linear Algebra and Its Applications ; Volume 435, Issue 1 , Sep , 2011 , Pages 186-192 ; 00243795 (ISSN) ; Jalili, M ; Hasler, M ; Sharif University of Technology
2011
Abstract
This paper introduces the connection-graph-stability method and uses it to establish a new lower bound on the algebraic connectivity of graphs (the second smallest eigenvalue of the Laplacian matrix of the graph) that is sharper than the previously published bounds. The connection-graph-stability score for each edge is defined as the sum of the lengths of the shortest paths making use of that edge. We prove that the algebraic connectivity of the graph is bounded below by the size of the graph divided by the maximum connection-graph-stability score assigned to the edges
The multiplicity of Laplacian eigenvalue two in unicyclic graphs
, Article Linear Algebra and Its Applications ; Vol. 445 , 2014 , pp. 18-28 ; Kiani, D ; Mirzakhah, M ; Sharif University of Technology
Abstract
Let G be a graph and L(G) be the Laplacian matrix of G. In this paper, we explicitly determine the multiplicity of Laplacian eigenvalue 2 for any unicyclic graph containing a perfect matching
On edge star sets in trees
, Article Discrete Mathematics ; Volume 311, Issue 13 , July , 2011 , Pages 1172-1178 ; 0012365X (ISSN) ; Ghorbani, E ; Mahmoodi, A ; Sharif University of Technology
2011
Abstract
Let A be a Hermitian matrix whose graph is G (i.e. there is an edge between the vertices i and j in G if and only if the (i,j) entry of A is non-zero). Let λ be an eigenvalue of A with multiplicity mA(λ). An edge e=ij is said to be Parter (resp., neutral, downer) for λ,A if mA(λ)-mA-e(λ) is negative (resp., 0, positive ), where A-e is the matrix resulting from making the (i,j) and (j,i) entries of A zero. For a tree T with adjacency matrix A a subset S of the edge set of G is called an edge star set for an eigenvalue λ of A, if |S|=mA(λ) and A-S has no eigenvalue λ. In this paper the existence of downer edges and edge star sets for non-zero eigenvalues of the adjacency matrix of a tree is...
A relation between the Laplacian and signless Laplacian eigenvalues of a graph
, Article Journal of Algebraic Combinatorics ; Volume 32, Issue 3 , 2010 , Pages 459-464 ; 09259899 (ISSN) ; Ghorbani, E ; Koolen, J. H ; Oboudi, M. R ; Sharif University of Technology
2010
Abstract
Let G be a graph of order n such that ∑n i=0(-1) iailambdan-i and ∑n i=0(-1) iailambdan-i are the characteristic polynomials of the signless Laplacian and the Laplacian matrices of G, respectively. We show that a i ≥b i for i=0,1,⋯,n. As a consequence, we prove that for any α, 0<α≤1, if q 1,⋯,q n and μ 1,⋯,μ n are the signless Laplacian and the Laplacian eigenvalues of G, respectively, then q 1 alpha+⋯+qα n≥μ α 1+⋯+μα n
On graphs whose star sets are (co-)cliques
, Article Linear Algebra and Its Applications ; Volume 430, Issue 1 , 2009 , Pages 504-510 ; 00243795 (ISSN) ; Ghorbani, E ; Mahmoodi, A ; Sharif University of Technology
Abstract
In this paper we study graphs all of whose star sets induce cliques or co-cliques. We show that the star sets of every tree for each eigenvalue are independent sets. Among other results it is shown that each star set of a connected graph G with three distinct eigenvalues induces a clique if and only if G = K1, 2 or K2, ..., 2. It is also proved that stars are the only graphs with three distinct eigenvalues having a star partition with independent star sets. © 2008 Elsevier Inc. All rights reserved
On the largest eigenvalue of signed unicyclic graphs
, Article Linear Algebra and Its Applications ; Volume 581 , 2019 , Pages 145-162 ; 00243795 (ISSN) ; Belardo, F ; Heydari, F ; Maghasedi, M ; Souri, M ; Sharif University of Technology
Elsevier Inc
2019
Abstract
Signed graphs are graphs whose edges get signs ±1 and, as for unsigned graphs, they can be studied by means of graph matrices. Here we focus our attention to the largest eigenvalue, also known as the index of the adjacency matrix of signed graphs. Firstly we give some general results on the index variation when the corresponding signed graph is perturbed. Also, we determine signed graphs achieving the minimal or the maximal index in the class of unbalanced unicyclic graphs of order n≥3. © 2019