Analyzing the Connectivity Potential of Landscape Geomorphic Systems: A Radar Remote Sensing and GIS Approach, Estufa Canyon, Texas, USA. (August 2005) ElSayed Ali Hermas Ibrahim, B.S., Mansoura University; M.S., Mansoura University Chair of Advisory Committee: Dr. John R. Giardino Connectivity is considered one of the fundamental aspects that influences the rate of mass movement in the landsca...

We derive sharp lower bounds for the first and the second Zagreb indices (M1 and M2 respectively) for trees and chemical trees with the given number of pendent vertices and find optimal trees. M1 is minimized by a tree with all internal vertices having degree 4, while M2 is minimized by a tree where each “stem” vertex is incident to 3 or 4 pendent vertices and one internal vertex, while the res...

The Randić index, R, also known as the connectivity or branching index, is an important topological index in chemistry. In order to attack some conjectures concerning the Randić index, Dvořák et al. [European J. Combin. 32 (2011), 434–442] introduced a modification of this index, denoted by R′. In this paper we present some of the basic properties of R′. We determine graphs with minimal and max...

A new parameter, related to and easily determined from the structure of a benzenoid system and that of a phenylene – the number of inlets (r) – is introduced. The connectivity (Randi}) index of both benzenoid systems and phenylenes is then shown to depend solely on the number of vertices and on r. A simple relation is established between the connectivity index of a phenylene and of the correspo...

In this article, a Quantitative structure Toxicity Relationships (QSTR) of twenty five phenol derivatives is presented. The QSTR study is mainly based on topological parameter. The topological parameter has been evaluated by CAChe prosoftware. The calculations of topological parameters have been done by MOPAC 2007. The statistical parameter has been calculated by SSP software. Various QSTR mode...

The variable Zagreb (v)M(2) index is introduced and applied to the structure-boiling point modeling of benzenoid hydrocarbons. The linear model obtained (the standard error of estimate for the fit model S(fit)=6.8 degrees C) is much better than the corresponding model based on the original Zagreb M2 index (S(fit)=16.4 degrees C). Surprisingly,the model based on the variable vertex-connectivity ...

Abstract The m-order connectivity index mχ(G) of an organic molecule whose molecular graph is G is the sum of the weights (di1di2 · · · dim+1) 1 2 , where di1di2 · · · dim+1 runs over all paths of length m in G and di denotes the degree of vertex vi. Dendrimer is a polimer molecule with a distinctive structure that resembles the crown of a tree. Dendrimers are key molecules in nanotechnology an...

A conjecture of AutoGraphiX on the relation between the Randić index R and the algebraic connectivity a of a connected graph G is: R a ≤ ( n− 3 + 2√2 2 ) / ( 2(1− cos π n ) ) with equality if and only if G is Pn, which was proposed by Aouchiche et al. [M. Aouchiche, P. Hansen and M. Zheng, Variable neighborhood search for extremal graphs 19: further conjectures and results about the Randić inde...

The Randić index of a graph G, denoted by R(G), is defined as the sum of 1/ √ d(u)d(v) over all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we partially solve two conjectures on the Randić index R(G) with relations to the diameter D(G) and the average distance μ(G) of a graph G. We prove that for any connected graph G of order n with minimum degree δ(G), if δ...

Let G be a simple connected graph in chemical graph theory and uν e = be an edge of G. The Randić index ( ) G χ and sum-connectivity ( ) G X of a nontrivial connected graph G are defined as the sum of the weights ν ud d 1 and ν u d d + 1 over all edges ν u e = of G, respectively. In this paper, we compute Randić ( ) G χ and sum-connectivity ( ) G X indices of V-phenylenic nanotubes and nanotori.