Yazar "Yilmaz, Fatih" 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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    The eigenvalues of a family of persymmetric anti-tridiagonal 2-Hankel matrices
    (ELSEVIER SCIENCE INC, 2013) Akbulak, Mehmet; da Fonseca, C. M.; Yilmaz, Fatih
    In this note we provide the general expression for the eigenvalues of a type of anti-tridiagonal matrices. (C) 2013 Elsevier Inc. All rights reserved.
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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 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.