Graph G is the square of graph H if two vertices x, y have an edge in G if and only if x, y are of distance at most two in H. Given H it is easy to compute its square H. Determining if a given graph G is the square of some graph is not easy in general. Motwani and Sudan [11] proved that it is NP-complete to determine if a given graph G is the square of some graph. The graph introduced in their ...

The purpose of this article is to present results that amount to a description of the conjugacy classes of three third–order root–finding iterative methods that do not require the use of second derivatives for their formulation, for complex polynomials of degrees two, three and four. For degrees two and three, a full description of the conjugacy classes is accomplished, in each case, by a one–p...

The effects of two water regimes (well-watered condition or drought stress) on root length,root surface area and root volume were tested on two peanut genotypes (the drought-resistantvariety HuaYu 22 (HY22) and the drought-sensitive variety HuaYu 23 (HY23)), measured 101days after sowing. The roots were sampled from the upper (0–40 cm) and deeper (40–100 cm)soil layers. Root diameter was measur...

The stability of a delay differential equation can be investigated on the basis of the root location of the characteristic function. Though a number of stability criteria are available, they usually do not provide any information about the characteristic root with maximal real part, which is useful in justifying the stability and in understanding the system performances. Because the characteris...

the aim of this case report was to present a case of multiple idiopathic apical root resorption which is a rare condition in a 17-year-old adult male. external root resorption of the permanent teeth is a multifactorial process. well-recognized causes of apical root resorption in permanent teeth include orthodontic therapy, trauma, periapical or periodontal inflammation, tumors, cysts, occlusal ...

ABSTRACT In gravitational microlensing formalism and for modelling binary light curves, the key step is solving lens equation. Currently, a combination of Newton’s Laguerre’s methods which was first introduced by Skowron & Gould (SG) used while curves. this paper, we introduce fast root-finding algorithm univariate polynomials based on Aberth–Ehrlich (AE) method developed in 1967 as an impr...

In this paper, four new ninth order iterative methods for solving nonlinear equations are constructed. It is proved that these methods have the convergence order of nine requiring six function evaluations per iteration. Numerical comparisons are included to demonstrate exceptional convergence speed of the proposed methods.