The topological indices, defined as the sum of contributions of all pairs of vertices (among which are the Wiener, Harary, hyper–Wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

Quasi-self-reciprocal polynomials (QSRP's), were introduced in [2] as a generalization of SRP's. They represent a superset of SRP's, since QSRP's are defined f*(x) = *f(x). This extends SRP's over GF (pk), p > 2, to include those for which f*(x) =-f(x). (15) Thus, if f(x) = x' +fr-ixr-' +f,-2x'-2 + a** +f,x + f,,, fnei =-fi, with f. =-1 since f(x) is manic. Polynomials defined by (15) are denot...

Let K be an algebraically closed field of characteristic zero and let f ∈ K[x]. The m-th cyclic resultant of f is rm = Res(f, x m − 1). A generic monic polynomial is determined by its full sequence of cyclic resultants; however, the known techniques proving this result give no effective computational bounds. We prove that a generic monic polynomial of degree d is determined by its first 2d+1 cy...

Abstract. We consider here a discrete system of spheres interacting through a lubrication force. This force is dissipative, and singular near contact: it behaves like the reciprocal of interparticle distance. We propose a macroscopic constitutive equation which is built as the natural continuous counterpart of this microscopic lubrication model. This model, which is of the newtonian type, relie...

the rotor of enegelberg whitener was equipped with a screw conveyor to reduce broken rice percentage. according to preliminary experiments this modification could reduce broken rice percentage about 2.5%. further experiment was performed to determine the effect of rotor speeds and blade positions on white rice quality. to do this, five rotor speeds, consisting 500, 600, 700, 800 and 900 r.p.m a...

The reciprocal complementary Wiener number of a connected graph G is defined as ( ) { } ( ) ( ) | ∑ u v V G RCW G d d u v G ⊆ = + − , 1 1 , where ( ) V G is the vertex set. ( ) | d u v G , is the distance between vertices u and v, and d is the diameter of G. A tree is known as a caterpillar if the removal of all pendant vertices makes it as a path. Otherwise, it is called a non-caterpillar. Amo...

In a seminal STOC’95 paper, Arya et al. [4] devised a construction that for any set S of n points in R and any ǫ > 0, provides a (1 + ǫ)-spanner with diameter O(log n), weight O(log n)w(MST (S)), and constant maximum degree. Another construction of [4] provides a (1 + ǫ)-spanner with O(n) edges and diameter α(n), where α stands for the inverse-Ackermann function. Das and Narasimhan [18] devised...

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and spatial clustering gives this model a range of interesting properties. Empirical degree distributions converge to a limit law, which can be a power law with...

The Wiener index of a graph is the sum of all pairwise distances of vertices of the graph. Fischermann et al [5] characterized the trees which minimize the Wiener index among all trees with the maximum degree at most ∆. They also determined the trees which maximize the Wiener index, but in a much more restricted family of trees which have two distinct vertex degrees only. In this note, we fully...