By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fai...

For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.

This paper presents a new and precise mo del for different kinds of eccentric rotor of rotating machines based on polar signals concepts. Eccentricity faults in each static, dynamic and mixed cases cause that the non-uniform air-gap of machine be established. The applied model using polar signals for eccentric rotors have removed the usage approximations in two recent decays. Eccentricity coeff...

Nomenclature a = semi-major axis ; e = eccentricity ; ν = true anomaly ; φ(ν) = fundamental matrix of relative motion ; B(ν) = input matrix in the dynamic model of relative motion ; R(ν) = φ(ν)B(ν) = φ(ν)B(ν) = primer vector evolution matrix ; uf = φ(νf )Xf − φ(ν1)X1 6= 0 = boundary conditions ; N = number of velocity increments ; νi, ∀ i = 1, · · · , N = impulses application times ; ∆vi = impu...

The reconfiguration graph R k ( G ) for the -colorings of a has as vertex set all possible and two colorings are adjacent if they differ in color exactly one . Let d , ? 1 be integers such that + We prove every ? > 0 with n vertices maximum average degree ? diameter O log ? This significantly strengthens several existing results.

Abstract We introduce a methodology based on averaging similarity matrices with the aim of integrating layers multiplex network into single monoplex network. Multiplex networks are adopted for modelling wide variety real-world frameworks, such as multi-type relations in social, economic and biological structures. More specifically, used when different nature (layers) arise between set elements ...

A measure of the degree of polarization for the three-dimensional polarization matrix (coherence matrix) of an electromagnetic field is proposed, based on Rayleigh scattering. The degree of polarization at a point is defined as an average, over all scattering directions, of an imagined dipole scattering of the three-dimensional state of polarization. This gives a well-defined purity measure, wh...

The eccentricity matrix ε(G) of a graph G is constructed from the distance by keeping only largest distances for each row and column. This can be interpreted as opposite adjacency obtained equal to 1 ε-eigenvalues are those its ε(G). Wang et al. [24] proposed problem determining maximum ε-spectral radius trees with given order. In this paper, we consider above n-vertex diameter. fixed odd diame...