In this paper, we present new results relating the numerical range of a matrix A with generalized Levinger transformation L(A, α, β) = αH A + βS A , where H A and S A , are, respectively the Hermitian and skew-hermitian parts of A. Using these results, we, then derive expressions for eigenvalues and eigenvectors of the perturbed matrix A + L(E, α, β), for a fixed matrix E and α, β are real para...

The main objective of Image processing is to convert an image into digital form and perform some operations on it, in order to get an enhanced image or to extract some useful information from it. But when they are needed to be converted into electronic form, it has to be done through scanning. One of the major problems in this field is that if the document to be read is not placed at 90. This w...

Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. One of the useful indic...

We prove a conjecture about the vertices and edges of the exchange graph of a cluster algebra A in two cases: when A is of geometric type and when A is arbitrary and its exchange matrix is nondegenerate. In the second case we also prove that the exchange graph does not depend on the coefficients of A. Both conjectures were formulated recently by Fomin and Zelevinsky. 1. Main definitions and res...

The set {bi}i=1 is called basis of L, and is represented by a matrix B having as columns the bi’s. Each matrix of the form BP , with P ∈ GLn(Z), represents a basis of L. A lattice can have bases with arbitrarily long and skew vectors. See figure 1. By lattice basis reduction we mean solving the following problem: given a lattice basis formed by long (and probably skew) vectors, compute a basis ...

Gain graphs are where the edges given some orientation and labeled with elements (called gains) from a group so that gains inverted when we reverse direction of edges. Generalizing notion gain graphs, skew have property reversed edge is image under an anti-involution. In this paper, study two different types, Laplacian g -Laplacian matrices for graph taken multiplicative F x field characteristi...

Two digraphs of same order are said to be skew-equienergetic if their skew energies are equal. One of the open problems proposed by Li and Lian was to construct non-cospectral skew-equienergetic digraphs on n vertices. Recently this problem was solved by Ramane et al. In this  paper, we give some new methods to construct new skew-equienergetic digraphs.

In this paper we develop lower bounds for the spectral radius of symmetric , skew{symmetric, and arbitrary real matrices. Our approach utilizes the well{known Leverrier{Faddeev algorithm for calculating the co-eecients of the characteristic polynomial of a matrix in conjunction with a theorem by Lucas which states that the critical points of a polynomial lie within the convex hull of its roots....