the noncommuting graph $nabla (g)$ of a group $g$ is asimple graph whose vertex set is the set of noncentral elements of$g$ and the edges of which are the ones connecting twononcommuting elements. we determine here, up to isomorphism, thestructure of any finite nonabeilan group $g$ whose noncommutinggraph is a split graph, that is, a graph whose vertex set can bepartitioned into two sets such t...

A graph is called integral if all its eigenvalues are integers. The quest for integral graphs was initiated by F. Harary and A. J. Schwenk [9]. All such cubic graphs were obtained by D. Cvetković and F. C. Bussemaker [2, 1], and independently by A. J. Schwenk [10]. There are exactly thirteen cubic integral graphs. In fact, D. Cvetković [2] proved that the set of regular integral graphs of a fix...

The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions C(i)(t) and of their instantaneous frequency ω(i)(t). On the basis of this decomposition we define the ω-conditioned statistical moments of the C(i) modes, named q-orde...

We present here a detailed time-dependent density-functional theory investigation aimed at systematically dissecting the electronic spectra of two thiolate and phosphine protected undecagold nanoclusters. Calculations performed on the experimental structures of Au11(PPh3)7Cl3 and Au11(PPh3)7(SPyr)3 show that ligands have negligible contributions in the visible region. Metal → ligand charge tran...

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

let $g$ be an $(n,m)$-graph. we say that $g$ has property $(ast)$if for every pair of its adjacent vertices $x$ and $y$, thereexists a vertex $z$, such that $z$ is not adjacentto either $x$ or $y$. if the graph $g$ has property $(ast)$, thenits complement $overline g$ is connected, has diameter 2, and itswiener index is equal to $binom{n}{2}+m$, i.e., the wiener indexis insensitive of any other...

let $d$ be a digraph with skew-adjacency matrix $s(d)$‎. ‎the skew‎ ‎energy of $d$ is defined as the sum of the norms of all‎ ‎eigenvalues of $s(d)$‎. ‎two digraphs are said to be skew‎ ‎equienergetic if their skew energies are equal‎. ‎we establish an‎ ‎expression for the characteristic polynomial of the skew‎ ‎adjacency matrix of the join of two digraphs‎, ‎and for the‎ ‎respective skew energ...

Setting up a system for first order results is straightforward. One can easily identify the major constituents in simple samples and obtain approximate concentrations. This is sufficient for some applications. However, second order effects are quite important for many applications. To obtain high accuracy, identify constituents with low concentrations, or operate on a wide variety of samples, s...

The prototropic exchange equilibria of two drugs, nizatidine (I) and ranitidine(II), and also of structurally related the N,N'-dimethyl-2-nitro-1,1-ethenediamine molecule (III) were investigated. From the changes in electronic spectra in media of various acidity several protonation constants were determined. For pK values were -0.82, 1.95, and 6.67; for ranitidine pK values were 1.95 and 8.13; ...

This thesis contains several new results about cycle spectra of graphs. The cycle spectrum of a graph G is the set of lengths of cycles in G. We focus on conditions which imply a rich cycle spectrum. We show a lower bound for the size of the cycle spectrum of cubic Hamiltonian graphs that do not contain a fixed subdivision of a claw as an induced subgraph. Furthermore, we consider cycle spectra...