the mathematical properties of nano molecules are an interesting branch of nanoscience forresearches nowadays. the periodic open single wall tubulene is one of the nano moleculeswhich is built up from two caps and a distancing nanotube/neck. we discuss how toautomatically construct the graph of this molecule and plot the graph by spring layoutalgorithm in graphviz and netwrokx packages. the sim...

As in the previous chapter, let us denote points in R by p = (x, y, z) and points in R by u = (u, v). An edge is then defined as the convex hull of (or, equivalently, the line segment between) two distinct points and a triangle as the convex hull of three non-collinear points. We will denote edges and triangles in R with capital letters and those in R with small letters, for example, e = [u1,u2...

the edge versions of reverse wiener indices were introduced by mahmiani et al. veryrecently. in this paper, we find their relation with ordinary (vertex) wiener index in somegraphs. also, we compute them for trees and tuc4c8(s) naotubes.

The vertex-edge Wiener polynomials of a simple connected graph are defined based on the distances between vertices and edges of that graph. The first derivative of these polynomials at one are called the vertex-edge Wiener indices. In this paper, we express some basic properties of the first and second vertex-edge Wiener polynomials of simple connected graphs and compare the first and second ve...

in this paper pi, szeged and revised szeged indices of an infinite family of ipr fullereneswith exactly 60+12n carbon atoms are computed. a gap program is also presented that isuseful for our calculations.

background: the p ulsatility index (pi) shows continuous blood flow to the end organs and is a significant factor believed to decrease in aortic coarctation. correction of this factor is of great importance in the treatment of stenotic lesions of the aorta. however, there are minimal data regarding the trend of changes in the pi after stent implantation. furthermore, the association between the...

background: in this study, we aimed to investigate the ability of transvaginal doppler ultrasonography in predicting in vitro fertilization (ivf) outcome in women undergoing this procedure. materials and methods: in this prospective observational study, 65 infertile women underwent ivf procedure in isfahan, during 2013-2014, were studied. the pulsatility index (pi), resistive index (ri) and pea...

topological indices are numerical parameters of a graph which characterize its topology. inthis paper the pi, szeged and zagreb group indices of the tetrameric 1,3–adamantane arecomputed.