the sharp upper bounds and the sharp lower bounds of the largest eigenvalues $lambda_1$, the least eigenvalue $lambda_n$, the second largest eigenvalue $lambda_2$, the spread and the separator among all firefly graphs on $n$ vertices are determined.

time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. the stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. it is well-known that the stabi...

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.

In this paper, we propose new approaches for solving the usefulskew tree (UST) routing problem [17]: Clock routing subject to general skew constraints. The clock layout synthesis engine of our UST algorithms is based on the deferred-merge embedding (DME) paradigm for zero-skew tree [5; 11 and bounded-skew tree [8; 21 routings; hence, the names UST/DME and Greedy-UST/DME for our algorithms. They...

Skew detection is an important stage of document image processing. It is desirable t o have a fast, all-purpose skew detector. This paper describes a fast skew detector using directional profile analysis. It can quickly and accurately detect skew on a wide variety of document images, including images with multiple text alignments and nontext regions. The complexity of the skew detection process...

Abstract. A skew edge coloring of a graph G is defined to be a set of two edge colorings such that no two edges are assigned the same unordered pair of colors. The skew chromatic index s(G) is the minimum number of colors required for a skew edge coloring of G. In this paper, an algorithm is determined for skew edge coloring of circular ladder graphs. Alsothe skew chromatic index of circular la...

Circular bacterial chromosomes have highly polarized nucleotide composition in the two replichores, and this genomic strand asymmetry can be visualized using GC skew graphs. Here we propose and discuss the GC skew index (GCSI) for the quantification of genomic compositional skew, which combines a normalized measure of fast Fourier transform to capture the shape of the skew graph and Euclidean d...

Process-variation induced skew has become one of the major contributors to the clock-skew in advanced technologies. Since process-variation induced skew is roughly proportional to clock-delay, it is preferable to design zero-skew clock-trees and have minimum clock-delay to reduce both unintentional and process-variation induced skews. In this paper, we propose a zero-skew buffered clock-tree sy...

Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.

In this paper, we discuss a new generalization of univariate skew-Cauchy distribution with two parameters, we denoted this by GSC(&lambda1, &lambda2), that it has more flexible than the skew-Cauchy distribution (denoted by SC(&lambda)), introduced by Behboodian et al. (2006). Furthermore, we establish some useful properties of this distribution and by two numerical example, show that GSC(&lambd...