The Laplacian and normalized Laplacian energy of G are given by expressions EL(G) = ∑n i=1 |μi − d|, EL(G) = ∑n i=1 |λi − 1|, respectively, where μi and λi are the eigenvalues of Laplacian matrix L and normalized Laplacian matrix L of G. An interesting problem in spectral graph theory is to find graphs {L,L}−noncospectral with the same E{L,L}(G). In this paper, we present graphs of order n, whi...

a multicone graph is defined to be join of a clique and a regular graph. a graph $ g $ is  cospectral with  graph $ h $ if their adjacency matrices have the same eigenvalues. a graph $ g $ is  said to be  determined by its spectrum or ds for short, if for any graph $ h $ with $ spec(g)=spec(h)$, we conclude that $ g $ is isomorphic to $ h $. in this paper, we present new classes of  multicone g...

This paper compares the Portuguese and Bulgarian consumer price indices (CPI) and attempts to identify some areas in which the CPI compilation methodology could be improved in the two countries. This work is organised into six sections. The first section briefly describes the organisational structure on which the production of the CPI is based in the two countries. The second section focuses on...

Let G be a connected graph of order n with Laplacian eigenvalues [Formula: see text]. The Laplacian-energy-like invariant of G, is defined as [Formula: see text]. In this paper, we investigate the asymptotic behavior of the 3.6.24 lattice in terms of Laplacian-energy-like invariant as m, n approach infinity. Additionally, we derive that [Formula: see text], [Formula: see text] and [Formula: see...

We spell out a formal equivalence between the naive Laplacian editing and semi-supervised learning by bi-Laplacian Regularized Least Squares. This allows us to write the solution to Laplacian mesh editing in a closed form, based on which we introduce the Generalized Linear Editing (GLE). GLE has both naive Laplacian editing and gradient based editing as special cases. GLE allows using diffusion...

Let η(G) denote the distance signless Laplacian spectral radius of a connected graph G. In this paper, bounds for the distance signless Laplacian spectral radius of connected graphs are given, and the extremal graph with the minimal distance signless Laplacian spectral radius among the graphs with given vertex connectivity and minimum degree is determined. Furthermore, the digraph that minimize...

Calculation of watermarking capacities of private Laplacian watermarking systems with the magnitude-error distortion measure under fixed attacks is addressed. First, in the case of an additive Laplacian attack, a nice closed-form formula for the watermarking capacities is derived, which involves only the distortion level and the parameter of the Laplacian attack. Second, in the case of an arbit...

A new formulation of Randić index is carried out as a minimization of a quadratic form which involves the Laplacian matrix of a graph. Using this formulation it is easy to realize that Randić index is useful in defining a new index of irregularity, which is then formulated here. A new context for the study of irregularity of graphs is advanced as a necessity for studying complex (biological) ne...

where Dui/Dt denotes the time derivative following the motion of the fluid particle, and ui is velocity. Here, ν is the kinematic viscosity, ∇x ≡ ∂xn∂xn is the Laplacian operator, ∂ denotes differentiation with respect to the subscript variable, summation is implied by repeated indices, p is pressure divided by fluid density; density is constant. ε is energy dissipation rate per unit mass of fl...