PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014), 2015
The D-eigenvalues µ 1 , µ 2 , . . . , µ n of a connected graph G are the eigenvalues of its dista... more The D-eigenvalues µ 1 , µ 2 , . . . , µ n of a connected graph G are the eigenvalues of its distance matrix. The distance Estrada index of G is defined in as In this paper, we give better lower bounds for the distance Estrada index of any connected graph as well as some relations between DEE (G) and the distance energy.
At this paper, we derive some relationships between permanents of one type of lower-Hessenberg ma... more 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.
Springer proceedings in mathematics & statistics, 2017
In this study, we get a general expression for the entries of the sth power of even order pentadi... more In this study, we get a general expression for the entries of the sth power of even order pentadiagonal 2-Toeplitz matrices.
In this paper, we derive the general expression of the r th power (r ∈ N) for one type of tridiag... more In this paper, we derive the general expression of the r th power (r ∈ N) for one type of tridiagonal matrix.
In this paper, we obtain a general expression for the entries of the rth (r ∈ Z) power of a certa... more In this paper, we obtain a general expression for the entries of the rth (r ∈ Z) power of a certain n × n complex tridiagonal matrix. In addition, we get the complex factorizations of Fibonacci polynomials, Fibonacci and Pell numbers.
The D-eigenvalues µ 1 , µ 2 , . . . , µ n of a connected graph G are the eigenvalues of its dista... more The D-eigenvalues µ 1 , µ 2 , . . . , µ n of a connected graph G are the eigenvalues of its distance matrix. The distance Estrada index of G is defined in as In this paper, we give better lower bounds for the distance Estrada index of any connected graph as well as some relations between DEE (G) and the distance energy.
In this paper, another proof of Pell identities is presented by using the determinant of tridiago... more In this paper, another proof of Pell identities is presented by using the determinant of tridiagonal matrices. It is calculated via the Laplace expansion.
In this paper, we compose a computational algorithm for the determinant and the inverse of the n ... more In this paper, we compose a computational algorithm for the determinant and the inverse of the n × n cyclic nonadiagonal matrix. The algorithm is suited for implementation using computer algebra systems (CAS) such as Mathematica and Maple.
In this paper, we compute the spectral norms of the matrices related with integer squences and we... more In this paper, we compute the spectral norms of the matrices related with integer squences and we give some example related with Fibonacci, Lucas, Pell and Perrin numbers.
For a simple graph G and a real number α (α = 0, 1) the graph invariant s α (G) is equal to the s... more For a simple graph G and a real number α (α = 0, 1) the graph invariant s α (G) is equal to the sum of powers of signless Laplacian eigenvalues of G. In this note, we present some new bounds on s α (G). As a result of these bounds, we also give some results on incidence energy.
In this study, an algorithm for computing the inverse of periodic k banded matrices , which are n... more In this study, an algorithm for computing the inverse of periodic k banded matrices , which are needed for solving the differential equations by using the finite differences, the solution of partial differential equations and the solution of boundary value problems is obtained and the inverses of periodic anti k banded matrices are computed. In addition, the determinant of these type of matrices and the solution of linear systems having these coefficient matrices are investigated. When obtaining this algorithm, the LU factorization is used.The algorithm is implementable to the CAS (Computer Algebra Systems) such as Maple and Mathematica.
In the present paper, we define two directed pseudo graph. Then, we investigate the adjacency mat... more In the present paper, we define two directed pseudo graph. Then, we investigate the adjacency matrices of the defined graphs and show that the permanents of the adjacency matrices are Jacobsthal and Jacobsthal-Lucas numbers. We also give complex factorization formulas for the Jacobsthal sequence.
We consider the weighted digraphs in which the arc weights are positive definite matrices. We obt... more We consider the weighted digraphs in which the arc weights are positive definite matrices. We obtain some upper bounds for the spectral radius of these digraphs and characterize the digraphs achieving the upper bounds. Some known upper bounds are then special cases of our results.
In this paper, we derive a general expression for mth powers of symmetric (0, 1)-heptadiagonal ma... more In this paper, we derive a general expression for mth powers of symmetric (0, 1)-heptadiagonal matrices with n = 3k order, n ∈ N (k = 1, 2, 3, ..., n/3).
In this paper, we derive a general expression for mth powers of symmetric (0, 1)-heptadiagonal ma... more In this paper, we derive a general expression for mth powers of symmetric (0, 1)-heptadiagonal matrices with n = 3k order, n ∈ N (k = 1, 2, 3, ..., n/3).
In this paper, we compute the spectral norms of the matrices related with integer squences and we... more In this paper, we compute the spectral norms of the matrices related with integer squences and we give two examples related with Fibonacci and Lucas numbers.
A proof of an identity for a generalization of well-known number sequences
In this study, we give an identity for known special number sequences then prove it using Laplace... more In this study, we give an identity for known special number sequences then prove it using Laplace expansion formula.
Recently there is huge interest in graph theory and intensive study on computing integer powers o... more 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.
In this paper, we derive the general expression of the r-th power for some n-square complex tridi... more In this paper, we derive the general expression of the r-th power for some n-square complex tridiagonal matrices.Also one type is given eigenvalues and eigenvectors of complex anti-tridiagonal matrices Additionally, we obtain the complex factorizations of Fibonacci polynomials.
In this study, we get a general expression for the entries of the sth power of even order pentadi... more In this study, we get a general expression for the entries of the sth power of even order pentadiagonal 2-Toeplitz matrices.
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