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Öğe Improved Bounds for the Spectral Radius of Digraphs(Hacettepe Univ, Fac Sci, 2010) Bozkurt, Şerife Burcu; Güngör, A. DilekLet G = (V, E) be a digraph with n vertices and m, arcs without loops and multi-arcs. The spectral radius rho(G) of G is the largest eigenvalue of its adjacency matrix. In this note, we obtain two sharp upper and lower bounds on rho(G). These bounds improve those obtained by G. H. Xu and C.-Q Xu (Sharp bounds for the spectral radius of digraphs, Linear Algebra Appl. 430, 1607-1612, 2009).Öğe Improved Upper and Lower Bounds for the Spectral Radius of Digraphs(Elsevier Science Inc, 2010) Güngör, A. Dilek; Das, Kinkar Ch.Let G be a digraph with n vertices and m arcs without loops and multiarcs. The spectral radius rho(G) of G is the largest eigenvalue of its adjacency matrix. In this paper, sharp upper and lower bounds on rho(G) are given. We show that some known bounds can be obtained from our bounds.Öğe Lower bounds for the norms of hilbert matrix and hadamard product of cauchy-toeplitz and cauchy-hankel matrices(2004) Güngör, A. Dilek; Sinan, AliIn this study, we have found lower bounds for the spectral norms and Euclidean norms of Hilbert matrix H(1/(ij-1))_{i,j1}n and its Hadamard square root H(1/(ij-1){1/2})_{i,j1}n In addition, we have established lower bounds for the spectral norms and Euclidean norms of the Hadamard product of Cauchy-Toeplitz and Cauchy-Hankel matrices.Öğe Lower bounds fort he norms of Hilbert Matrix and Hadamard Product of Cauchy-Toeplitz and Cauchy-Hankel Matrices(Selcuk University Research Center of Applied Mathematics, 2004) Güngör, A. Dilek; Sinan, AliIn this study, we have found lower bounds for the spectral norms and Euclidean norms of Hilbert matrix H=(1/ (i+j-1) )_{i,j=1}? and its Hadamard square root H=(1/(i+j-1)^{1/2})_{i,j=1}?.In addition, we have established lower bounds for the spectral norms and Euclidean norms of the Hadamard product of Cauchy-Toeplitz and Cauchy-Hankel matrices.Öğe A New Example of Deficiency One Groups(Amer Inst Physics, 2010) Çevik, A. Sinan; Güngör, A. Dilek; Karpuz, Eylem G.; Ateş, Fırat; Cangül, I. NaciThe main purpose of this paper is to present a new example of deficiency one groups by considering the split extension of a finite cyclic group by a free abelian group having rank two.Öğe A New Like Quantity Based on "Estrada Index"(Springer International Publishing Ag, 2010) Güngör, A. DilekWe first define a new Laplacian spectrum based on Estrada index, namely, Laplacian Estrada-like invariant, LEEL, and two new Estrada index-like quantities, denoted by S and EEX, respectively, that are generalized versions of the Estrada index. After that, we obtain some lower and upper bounds for LEEL, S, and EEX.Öğe Note on the Distance Energy of Graphs(UNIV KRAGUJEVAC, FAC SCIENCE, 2010) Bozkurt, Ş. Burcu; Güngör, A. Dilek; Zhou, BoThe distance energy of a graph G is defined as the sum of the absolute values of the eigenvalues of the distance matrix of G. In this note, we obtain an upper bound for the:distance energy of any connected graph G. Specially, we present upper bounds for the distance energy of connected graphs of diameter 2 with given numbers of vertices and edges, and unicyclie graphs with odd girth. Additionally, we give also a lower bound for the distance energy of unicyclic graphs with odd girth.Öğe On Kirchhoff Index and Resistance-Distance Energy of a Graph(Univ Kragujevac, Fac Science, 2012) Das, Kinkar Ch; Güngör, A. Dilek; Çevik, A. SinanWe report lower hounds for the Kirchhoff index of a connected (molecular) graph in terms of its structural parameters such as the number of vertices (atoms), the number of edges (bonds), maximum vertex degree (valency), second maximum vertex degree and minimum vertex degree. Also we give the Nordhaus-Gaddum-type result for Kirchhoff index. In this paper we define the resistance distance energy as the sum of the absolute values of the eigenvalues of the resistance distance matrix and also we obtain lower and upper bounds for this energy.Öğe On the Efficiency of Semi-Direct Products of Finite Cyclic Monoids by One-Relator Monoids(Amer Inst Physics, 2010) Ateş, Fırat; Karpuz, Eylem Güzel; Güngör, A. Dilek; Çevik, A. Sinan; Cangül, İsmail NaciIn this paper we give necessary and sufficient conditions for the efficiency of a standard presentation for the semi-direct product of finite cyclic monoids by one-relator monoids.Öğe On the Harary Energy and Harary Estrada Index of a Graph(Univ Kragujevac, Fac Science, 2010) Güngör, A. Dilek; Çevik, A. SinanThe main purposes of this paper are to introduce and investigate the Harary energy and Harary Estrada index of a graph. In addition we establish upper and lower bounds for these new energy and index separately.Öğe On the Norms of Toeplitz and Hankel Matrices With Pell Numbers(Amer Inst Physics, 2010) Karpuz, Eylem Güzel; Ateş, Fırat; Güngör, A. Dilek; Cangül, İsmail Naci; Çevik, A. SinanLet us define A = [a(ij)](i,j=0)(n-1) and B = [b(ij)](i,j=0)(n-1) as n x n Toeplitz and Hankel matrices, respectively, such that a(ij) = Pi-j and b(ij) = Pi+j, where P denotes the Pell number. We present upper and lower bounds for the spectral norms of these matrices.Öğe Primes in Z[exp(2?i/3)](Amer Inst Physics, 2010) Namlı, Dilek; Cangül, İsmail Naci; Çevik, Ahmet Sinan; Güngör, A. Dilek; Tekcan, AhmetIn this paper, we study the primes in the ring Z[w], where w = exp(2 pi i/3) is a cubic root of unity. We gave a classification of them and some results related to the use of them in the calculation of cubic residues are obtained.Öğe Randic Matrix and Randic Energy(Univ Kragujevac, Fac Science, 2010) Bozkurt, Ş. Burcu; Güngör, A. Dilek; Gutman, Ivan; Çevik, A. SinanIf G is a graph on n vertices, and d(i) is the degree of its i-th vertex, then the Randic matrix of G is the square matrix of order n whose (i, j)-entry is equal to 1/root d(i) d(j) di if the i-th and j-th vertex of G are adjacent, and zero otherwise. This matrix in a natural way occurs within Laplacian spectral theory, and provides the non-trivial part of the so-called normalized Laplacian matrix. In spite of its obvious relation to the famous Randic index, the Randic matrix seems to have not been much studied in mathematical chemistry. In this paper we define the Randic energy as the sum of the absolute values of the eigenvalues of the Randic matrix, and establish mine of its properties, in particular lower and upper bounds for it.Öğe Randic Spectral Radius and Randic Energy(Univ Kragujevac, Fac Science, 2010) Bozkurt, Ş. Burcu; Güngör, A. Dilek; Gutman, IvanLet G be a simple connected graph with n vertices and let d(i) be the degree of its i-th vertex. The Randic matrix of G is the square matrix of order n whose (i, j)-entry is equal to 1/root d(i)d(j) di if the i-th and j-th vertex of G are adjacent, and zero otherwise. The Randic eigenvalues are the eigenvalues of the Rancho matrix. The greatest Randic eigenvalue is the Randic spectral radius of C. The Randic energy is the sum of the absolute values of the Randic eigenvalues. Lower bounds for Randic spectral radius and an upper bound for Randic energy are obtained. Graphs for which these bounds are best possible are characterized.Öğe Some Bounds for the Product of Singular Values(2005) Güngör, A. DilekLet A be an nx n complex matrix with 01 (4) 2 02 (A) > on (A) and let 1 < k < In. Bounds for 01 (A)...Ok (4), ok (4)...0 (A) and On-k+1 (4) On (A), involving k, n, r (A) ((4)), a; and det A where r; (c. (A)) is the Euclidean norm of the i-th row (column) of A and a,'s are positive real numbers such that a+a² + += n. are presented.
