Académie serbe des sciences et des arts-2004 Classe des sciences mathématiques et naturelles sciences mathématiques, N o 29 A b s t r a c t. The generalized inverse L † of the Laplacian matrix of a connected graph is examined and some of its properties are established. In some physical and chemical considerations the quantity r ij = (L †) ii + (L †) jj − (L †) ij − (L †) ji is encountered; it i...

vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdo...

The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph. Its considerable applications are found in a variety of fields. In this paper, we determine the maximum value of Kirchhoff index among the unicyclic graphs with fixed number of vertices and maximum degree, and characterize the corresponding extremal graph.

Drought resistance breeding provides a hopeful way to improve yield and quality of wheat in arid and semiarid regions. Constructing core collection is an efficient way to evaluate and utilize drought-resistant germplasm resources in wheat. In the present research, 1,683 wheat varieties were divided into five germplasm groups (high resistant, HR; resistant, R; moderate resistant, MR; susceptible...

The resistance to fumigant insecticides in stored-products insects is often recorded. Several factors influence the evolution of insecticide resistance. Among these, the frequency of applications and the migration of resistant populations are of primary importance for the stored-product insects. The aim of this study was to characterize the spectrum and investigate the status of phosphine resis...

We investigate the behavior of electric potentials on distance-regular graphs, and extend some results of a prior paper, [12]. Our main result, Theorem 4 below, shows(together with Corollary 3) that if distance is measured by the electric resistance between points then all points are close to being equidistant on a distance-regular graph with large valency. A number of auxiliary results are als...

The electrical structure of the power grid is utilized to address the phasor measurement unit (PMU) placement problem. First, we derive the connectivity matrix of the network using the resistance distance metric and employ it in the linear program formulation to obtain the optimal number of PMUs, for complete network observability without zero injection measurements. This approach was developed...

functionally graded aluminium/zirconia metal matrix composite was fabricated using stir casting technique followed by horizontal centrifugal casting process and a hollow cylindrical functionally graded composite (150 x 150 x 16 mm) was obtained with centrifuging speed of 1200 rpm. the microstructural evaluation and hardness test was carried out on the outer and inner surface of the functionally...

From contactless payments to remote car unlocking, many applications are vulnerable to relay attacks. Distance bounding protocols are the main practical countermeasure against these attacks. In this paper, we present a formal analysis of SKI, which recently emerged as the first family of lightweight and provably secure distance bounding protocols. More precisely, we explicate a general formalis...

We study the family of p-resistances on graphs for p ≥ 1. This family generalizes the standard resistance distance. We prove that for any fixed graph, for p = 1 the p-resistance coincides with the shortest path distance, for p = 2 it coincides with the standard resistance distance, and for p → ∞ it converges to the inverse of the minimal s-t-cut in the graph. Secondly, we consider the special c...