given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

We have examined steady-state and time-resolved luminescence properties of CdS:Te quantum dots (QDs). The transient emission spectra have a red shift along the emission process. Using singular value decomposition and multiexponential decay analysis, the luminescence is found to originate from two distinct and parallel channels: band-edge excitonic emission and trapping state emission. With incr...

This work introduces a new approach to inverse halftoning using nonorthogonal wavelets. The distinct features of this wavelet-based approach are: 1) edge information in the highpass wavelet images of a halftone image is extracted and used to assist inverse halftoning, 2) cross-scale correlations in the multiscale wavelet decomposition are used for removing background halftoning noise while pres...

We consider the rational linear relations between real numbers whose squared trigonometric functions have rational values, angles we call " geodetic ". We construct a convenient basis for the vector space over Q generated by these angles. Geodetic angles and rational linear combinations of geodetic angles appear naturally in Euclidean geometry; for illustration we apply our results to equidecom...

Geodetic sets in graphs are briefly surveyed. After an overview of earlier results, we concentrate on recent studies of the geodetic number and related invariants in graphs. Geodetic sets in Cartesian products of graphs and in median graphs are considered in more detail. Algorithmic issues and relations with several other concepts, arising from various convex and interval structures in graphs, ...

The geodetic problem was introduced by Harary et al. [17]. In order to model some social network problems, a similar problem is introduced in this paper and named the strong geodetic problem. The problem is solved for complete Apollonian networks. It is also proved that in general the strong geodetic problem is NP-complete.

An undirected graph G = (V;E) is said to be geodetic, if between any pair of vertices x; y 2 V there is a unique shortest path. Generalizations of geodetic graphs are introduced in this paper. K-geodetic graphs are de ned as graphs in which every pair of vertices has at most k paths of minimum length between them. Some properties and characterizations of k{geodetic graphs are studied.

A set of vertices S in a graph is called geodetic if every vertex of this graph lies on some shortest path between two vertices from S. In this paper, minimum geodetic sets in median graphs are studied with respect to the operation of peripheral expansion. Along the way geodetic sets of median prisms are considered and median graphs that possess a geodetic set of size two are characterized. © 2...

Let R be a commutative ring with $Z(R)$ its set of zero-divisors. In this paper, we study the total graph of $R$, denoted by $T(Gamma(R))$. It is the (undirected) graph with all elements of R as vertices, and for distinct $x, yin R$, the vertices $x$ and $y$ are adjacent if and only if $x + yinZ(R)$. We study the chromatic number and edge connectivity of this graph.

Let K be a family of graphs. A K-decomposition, D , of a graph H (called the host) is a partition of the edges of H such that the subgraph induced by each part of the partition (called blocks) is isomorphic to an element of K. The chromatic index of the decomposition, denoted χ′(D), is the minimum number of colors required to color each block in the decomposition so that blocks that share a com...