Şerife Büyükköse

A proof of a conjecture on monotonic behavior of the largest eigenvalue of a number-theoretic matrix

In this study we investigate the monotonic behavior of the largest eigenvalue of the n×n matrix EnTEn, where the i j− entry of En is 1 if j|i and 0 otherwise and hence we present a proof of a part of the Mattila-Haukkanen conjecture [16]. MSC2010. 15A18, 15A42, 11A25

Determinants and inverses of circulant matrices with complex Fibonacci numbers

Abstract Let ℱn = circ (︀F*1 , F*2, . . . , F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers F*1, F*2, . . . , F*n. In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci numbers. Furthermore, we show that ℱn is invertible and obtain the entries of the inverse of ℱn in terms of complex Fibonacci numbers.

A Note on the Spectral Radius of Weighted Signless Laplacian Matrix

A weighted graph is a graph that has a numeric label associated with each edge, called the weight of edge. In many applications, the edge weights are usually represented by nonnegative integers or square matrices. The weighted signless Laplacian matrix of a weighted graph is defined as the sum of adjacency matrix and degree matrix of same weighted graph. In this paper, a brief overview of the notation and concepts of weighted graphs that will be used throughout this study is given. In Section 2, the weighted signless Laplacian matrix of simple connected weighted graphs is considered, some upper bounds for the spectral radius of the weighted signless Laplacian matrix are obtained and some results on weighted and unweighted graphs are found.

On the Maximum Clique and the Maximum Independence Numbers of a Graph

In this paper we obtain some bounds for the clique number ω and the independence number α, in terms of the eigenvalues of the normalized Laplacian matrix of a graph G.