Yazar "Bozkurt, Durmus" seçeneğine göre listele

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    The Adjacency Matrix of One Type of Directed Graph and the Jacobsthal Numbers and Their Determinantal Representation
    (HINDAWI PUBLISHING CORPORATION, 2012) Yilmaz, Fatih; Bozkurt, Durmus
    Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we consider one type of directed graph. Then we obtain a general form of the adjacency matrices of the graph. By using the well-known property which states the (i, j) entry of A(m) (A is adjacency matrix) is equal to the number of walks of length m from vertex i to vertex j, we show that elements of mth positive integer power of the adjacency matrix correspond to well-known Jacobsthal numbers. As a consequence, we give a Cassini-like formula for Jacobsthal numbers. We also give a matrix whose permanents are Jacobsthal numbers.
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    Another proof of Pell identities by using the determinant of tridiagonal matrix
    (ELSEVIER SCIENCE INC, 2012) Yasar, Meral; Bozkurt, Durmus
    In this paper, another proof of Pell identities is presented by using the determinant of tridiagonal matrix. It is calculated via the Laplace expansion. (C) 2011 Elsevier Inc. All rights reserved.
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    Bounds on the Distance Energy and the Distance Estrada Index of Strongly Quotient Graphs
    (HINDAWI PUBLISHING CORPORATION, 2013) Bozkurt, S. Burcu; Adiga, Chandrashekara; Bozkurt, Durmus
    The notion of strongly quotient graph (SQG) was introduced by Adiga et al. (2007). In this paper, we obtain some better results for the distance energy and the distance Estrada index of any connected strongly quotient graph (CSQG) as well as some relations between the distance Estrada index and the distance energy. We also present some bounds for the distance energy and the distance Estrada index of CSQG whose diameter does not exceed two. Additionally, we show that our results improve most of the results obtained by Gungor and Bozkurt (2009) and Zaferani (2008).
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    Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas Numbers
    (ELSEVIER SCIENCE INC, 2012) Bozkurt, Durmus; Tam, Tin-Yau
    Let n >= 3 and let J(n) := circ(J(1),J(2),...,J(n)) and j(n) := circ(j(0),j(1),...,j(n-1)) be the n x n circulant matrices associated with the Jacobsthal numbers J(1),...,J(n) and the Jacobsthal-Lucas numbers j(0),...,j(n-1), respectively. The determinants and the inverses of J(n) and j(n) are obtained in terms of J(1),...,J(n) and j(1),...,j(n-1), respectively. (C) 2012 Elsevier Inc. All rights reserved.
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    Determinants and inverses of r-circulant matrices associated with a number sequence
    (TAYLOR & FRANCIS LTD, 2015) Bozkurt, Durmus; Tam, Tin-Yau
    Let W-n = circ(r) (W-1, W-2, ... , W-n) be the r -circulant matrix associated with the numbers defined by the recursive relation W-n = pW(n-1) + qW(n-2) with initial conditions W-0 = a and W-1 = b, where a, b, p, q is an element of Z and n >= 2. We obtain some formulas for the determinants and inverses of Wn. Some bounds for spectral norms of W-n are obtained as applications.
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    Hessenberg matrices and the Pell and Perrin numbers
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2011) Yilmaz, Fatih; Bozkurt, Durmus
    In this paper, we investigate the Pell sequence and the Perrin sequence and we derive some relationships between these sequences and permanents and determinants of one type of Hessenberg matrices. (C) 2011 Elsevier Inc. All rights reserved.
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    On Adjacency Matrix of One Type of Graph and Pell Numbers
    (INT ASSOC ENGINEERS-IAENG, 2011) Yilmaz, Fatih; Bozkurt, Durmus
    Recently there is huge interest on graph theory and intensive study on computing integer powers of matrices. As it is well-known, the (i,j)th entry of A(m) (arbitrary positive integer power of A) is just the number of the different paths from vertex i to vertex j. In the present paper, we consider adjacency matrix of one type of graph, which is a block-diagonal matrix, and we investigate relations between the matrix and well-known Pell sequence.
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    On Incidence Energy
    (UNIV KRAGUJEVAC, FAC SCIENCE, 2014) Bozkurt, S. Burcu; Bozkurt, Durmus
    The incidence energy of a graph is defined as the sum of singular values of its incidence matrix. In this paper, we establish some new bounds on the incidence energy of connected graphs.
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    On the complex factorization of the Lucas sequence
    (PERGAMON-ELSEVIER SCIENCE LTD, 2011) Bozkurt, S. Burcu; Yilmaz, Fatih; Bozkurt, Durmus
    In this paper, firstly we present a connection between determinants of tridiagonal matrices and the Lucas sequence. Secondly, we obtain the complex factorization of Lucas sequence by considering how the Lucas sequence can be connected to Chebyshev polynomials by determinants of a sequence of matrices. (C) 2011 Elsevier Ltd. All rights reserved.
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    On the Fibonacci and Lucas numbers, their sums and permanents of one type of Hessenberg matrices
    (HACETTEPE UNIV, FAC SCI, 2014) Yilmaz, Fatih; Bozkurt, Durmus
    At this paper, we derive some relationships between permanents of one type of lower-Hessenberg matrix family and the Fibonacci and Lucas numbers and their sums.
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    On the Fibonacciand Lucasnumbers, their sums and permanents of one type of Hessenberg matrices
    (2014) Yılmaz, Fatih; Bozkurt, Durmus
    Atthispaper,wederivesomerelationshipsbetweenpermanentsofone typeoflower-HessenbergmatrixfamilyandtheFibonacciandLucas numbersandtheirsums. 2000AMSClassification: 15A36,15A15,11B37
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    ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS
    (HACETTEPE UNIV, FAC SCI, 2008) Akbulak, Mehmet; Bozkurt, Durmus
    Let us define A = [a(ij)] and B = [b(ij)] as n x n Toeplitz matrices such that a(ij) equivalent to F(i-j) and b(ij) equivalent to L(i-j) where F and L denote the usual Fibonacci and Lucas numbers, respectively. We have found upper and lower bounds for the spectral norms of these matrices.
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    On the Number of Spanning Trees of Graphs
    (HINDAWI PUBLISHING CORPORATION, 2014) Bozkurt, S. Burcu; Bozkurt, Durmus
    We establish some bounds for the number of spanning trees of connected graphs in terms of the number of vertices (n), the number of edges (m), maximum vertex degree (Delta(1)), minimum vertex degree (delta), first Zagreb index (M-1), and Randic index (R-1).
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    On the order-m generalized Fibonacci k-numbers
    (PERGAMON-ELSEVIER SCIENCE LTD, 2009) Akbulak, Mehmet; Bozkurt, Durmus
    In this paper, we defined order-m generalized Fibonacci k-numbers by matrix representation. Using this matrix representation we obtained sums, some identities and the generalized Binet formula of generalized order-m Fibonacci k-numbers. (C) 2009 Elsevier Ltd. All rights reserved.
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    On the signless Laplacian spectral radius of digraphs
    (CHARLES BABBAGE RES CTR, 2013) Bozkurt, S. Burcu; Bozkurt, Durmus
    Let G = (V, E) be a digraph with n vertices and m arcs without loops and multiarcs, V = {v(1), v(2), ... , v(n)}. Denote the outdegree and average 2-outdegree of the vertex v(i) by d(i)(+) and m(i)(+), respectively. Let A (G) be the adjacency matrix and D (G) = diag (d(1)(+), d(2)(+), ... , d(n)(+)) be the diagonal matrix with outdegree of the vertices of the digraph G. Then we call Q (G) = D (G) + A (G) signless Laplacian matrix of G. In this paper, we obtain some upper and lower bounds for the spectral radius of Q (G) which is called signless Laplacian spectral radius of G. We also show that some bounds involving outdegrees and the average 2-outdegrees of the vertices of G can be obtained from our bounds.
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    On the spectral norms of the matrices connected to integer number sequences
    (ELSEVIER SCIENCE INC, 2013) Bozkurt, Durmus
    In this paper, we compute the spectral norms of the matrices related with integer sequences and we give two examples related with Fibonacci, Lucas, Pell and Perrin numbers. (C) 2013 Elsevier Inc. All rights reserved.
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    On the spectral radius and the energy of a digraph
    (TAYLOR & FRANCIS LTD, 2015) Bozkurt, S. Burcu; Bozkurt, Durmus; Zhang, Xiao-Dong
    The energy of a digraph D is defined as E (D) = Sigma(n)(i=1) vertical bar Re (z(i))vertical bar, where z(1), ... , z(n) are the (possibly complex) eigenvalues of D. In this paper, we obtain an improved lower bound on the spectral radius of D. Considering this result, we present an upper bound on the energy of D. We also show that our results generalize and improve some known results for graphs and digraphs.
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    Positive integer powers and inverse for one type of even order symmetric pentadiagonal matrices
    (ELSEVIER SCIENCE INC, 2013) Arslan, Saadet; Koken, Fikri; Bozkurt, Durmus
    In this study we derive the general expression for the entries of the qth power (q is an element of N) for one type of even order symmetric pentadiagonal matrices. (C) 2012 Elsevier Inc. All rights reserved.
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    Positive integer powers and inverse for one type of even order symmetric pentadiagonal matrices (vol 219, pg 5241, 2012)
    (ELSEVIER SCIENCE INC, 2013) Arslan, Saadet; Koken, Fikri; Bozkurt, Durmus
    [Abstract not Available]
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    Positive integer powers for one type of odd order circulant matrices
    (ELSEVIER SCIENCE INC, 2011) Koken, Fikri; Bozkurt, Durmus
    In this study we derive the general expression for the entries of the qth power q is an element of N for odd order complex circulant matrices of the type circ(n)(0, a, 0, ... , b). Crown Copyright (C) 2010 Published by Elsevier Inc. All rights reserved.