In this paper, a fundamentally new method, based on the definition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to the desired eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. These examples show an interesting phenomenon in the procedure: The diagonal matrix that converges to eigenvalues gives them in decreasing order in the sense of absolute value. Appendices A to C provide Matlab codes that implement the proposed algorithms. They show that the proposed algorithms are very easy to program.

In this paper, we derive the general expression for the entries of the positive Integer powers of the Min matrix A = [min{i, j}],i, j = 1, 2, . . ., n of arbitrary order. Also, we give Maple 18 procedures in order to verify our calculations.

So far, various components of image characteristics have been used for steganal-ysis, including the histogram characteristic function, adjacent colors distribution, and sample pair analysis. However, some certain steganography methods have been proposed that can thwart some analysis approaches through man- aging the embedding patterns. In this regard, the present paper is intended to introduce a new analytical method for detecting stego images, which is robust against some of the embedding patterns designed specifically to foil steganalysis attempts. The proposed approach is based on the analysis of the eigenvalues of the cover correlation matrix used for the purpose of the study. Image cloud partitioning, vertical correlation function computation, constellation of the correlated data, and eigenvalues examination are the major challenging stages of this analysis method. The proposed method uses the LSB plane of images in spatial domain, extendable to transform domain, to detect low embedding rates-a major concern in the area of the LSB steganography. The simulation results based on deviation detection and rate estimation methods indicated that the proposed approach outperforms some well-known LSB steganalysis methods, specically at low embedding rates.

A graph is called integral if all eigenvalues of its adjacency matrix are Integers. Given a subset S of a  nite group G, the bi-Cayley graph BCay(G; S) is a graph with vertex set G  f1; 2g and edge set ff(x; 1); (sx; 2)g j s 2 S; x 2 Gg. In this paper, we classify all  nite groups admitting a connected cubic integral bi-Cayley graph.

Let G be a simple graph with vertices v_1, . . ., v_n. The adjacency matrix of G denoted by A(G) is an n×n matrix whose the entry (i, j) is 1 if v_i and v_j are adjacent and is zero otherwise. By the eigenvalues of G we mean the eigenvalues of A(G). Let λ _1 (G)≥ λ _2 (G)≥ ⋯ ≥ λ _n (G) be the eigenvalues of G. In this paper we obtain some results related to graphs with at most three non-negative eigenvalues. We obtain all non-connected graphs with this property. In addition, we find some families of connected graphs with this property. In particular we study two following families of graphs: 1. Graphs such as G with exactly two positive eigenvalues and one zero eigenvalues. In other words graphs such as G with λ _1 (G)>0, λ _2 (G)>0, λ _3 (G)=0 and λ _4 (G)0, λ _2 (G)>0, λ _3 (G)>0 and λ _4 (G)

The aim of this paper is to determine an upper bound for the number of non-co-spectral permutation graphs in terms of automorphism group of a graph G. As a corollary, we determine the eigenvalues of all permutation graphs P (Cn), where  2 Aut(Cn).

In this paper, we study the eigenvalues of real tridiagonal 3-Toeplitz matrices of different order. When the order of a tridiagonal 3-Toeplitz matrix is n = 3k+ 2, the eigenvalues were found explicitly. Here, we consider the distribution of eigenvalues for a tridiagonal 3-Toeplitz matrix of orders n = 3k and n = 3k + 1. We explain our method by finding roots of a combination of Chebyshev polynomials of the second kind. This distribution solves the eigenproblem for Integer powers of such matrices.