In this survey article a brief account on the development of Padmakar-Ivan (PI) index in that applications of Padmakar-Ivan (PI) index in the fascinating field of nano-technology are discussed.

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.

Relative centricity RC values of vertices/atoms are calculated within the Distance Detour and Cluj-Distance criteria on their corresponding Shell transforms. The vertex RC distribution in a molecular graph gives atom equivalence classes, useful in interpretation of NMR spectra. Timed by vertex valences, RC provides a new index, called Centric Connectivity CC, which can be useful in the topologi...

In the extension of irregularity indices, Abdo et. al. [1] defined the total irregu-larity of a graph G = (V, E) as irrt(G) = 21 Pu,v∈V (G) du − dv, where du denotesthe vertex degree of a vertex u ∈ V (G). In this paper, we investigate the totalirregularity of trees with bounded maximal degree Δ and state integer linear pro-gramming problem which gives standard information about extremal trees a...

The augmented eccentric connectivity index of a graph which is a generalization of eccentric connectivity index is defined as the summation of the quotients of the product of adjacent vertex degrees and eccentricity of the concerned vertex of a graph. In this paper we established some relationships between augmented eccentric connectivity index and several other graph invariants like number of ...

background: doppler indices of umbilical artery are used as indicator of fetal well being. objective: to compare doppler parameters of umbilical artery including pulsatility index (pi) and resistance index (ri) in patients with preeclampsia with those of normal pregnancies and to evaluate the diagnostic characteristics of these parameters in preeclampsia. materials and methods: in a case contro...

the atom bond connectivity index of a graph is a new topological index was defined by e.estrada as abc(g)  uve (dg(u) dg(v) 2) / dg(u)dg(v) , where g d ( u ) denotes degreeof vertex u. in this paper we present some bounds of this new topological index.

The problem of illuminating a simple n-gon with cn, c < 1 πlights is open, whereas a lower bound of ⌊ 3 5 n⌋ is known. We provide an algorithm for placing π-lights, and experimental results that support the conjecture that ⌊ 3 5 n⌋ lights are also sufficient. We also prove that ⌊ 5 6 n⌋ π-lights suffice if some may be outward facing.