Alireza Ashrafi

The main purpose of this presentation is to review some basic mathematical properties of the augmented eccentric connectivity index and, where possible, to establish explicit formulas for certain classes of graphs. Usually they are obtained by diagonalization of the neighboring matrix of the molecular graph and are based on the so-called bi-lobal eigenvectors. All shortcomings were finally removed when we turned to the eigenvectors of the corresponding Laplace matrices.

In 1971, I proposed the topological index Z for characterizing the topological structure of the carbon atom skeleton of saturated hydrocarbon molecule [1]. The following diagram shows the important role of the Z-index to connect various algebraic and geometric properties using caterpillar graphs [5].

Reverse Wiener Index

The energy of a graph cannot be an odd integer

7]) The energy of a graph cannot be the square root of an odd integer

Introduction
Experimental 1. Data set

Molecular Descriptors

Wiener Index of Composite Graphs

Main Result
Introduction A simple graph
The eccentric Connectiv In this section we compute

Our research has shown that lipid composition varies between different cells and even between different organelles within the same cell. Lipid chains differ in length and degree of unsaturation, i.e. in the number of double bonds. Such transitions depend on the chain length and the degree of saturation (i.e. the number of double bonds in the chain).

There are also other variables such as electrostatic potential and chemical potentials of all components of biological systems. This is because a certain proportion of lipids are negatively charged and can be protonated. Data set and corresponding experimental and ANN predicted redox potential values at pH=7.0 (E7 (V)).

A good correlation for this plot confirms the ability of the ANN model to predict redox potential. The spread of the residuals on both sides of the zero line indicates that there is no systematic error in the developed ANN model. In this paper, we calculate the number of possible positional isomers and chiral isomers of the hetero-fullerenes using Pólya's theorem.

An important invariant of connected graphs is the Wiener index, which is equal to the sum of the distances between all pairs of vertices of the corresponding graph. introduced the notion of the y-Wiener index of graphs as a generalization of the classical Wiener index and the hyperWiener index of graphs. The eccentricity index of molecular graph connectivity G, ξc(G), was proposed by Sharma, Goswami and Madan8.

It is defined as ξc(G) = Σu∈V(G)degG(u)ecc(u), where degG(x) denotes the degree of the vertex x in G and ecc(u) = Max{d(x, u ) | x∈ V(G)} . The radius and diameter of G are defined as the minimum and maximum eccentricity, respectively, among vertices of G. The eccentricity connectivity index of the molecular graph G, ξc(G), was proposed by Sharma, Goswami, and Madan.

Table 1. The data set and corresponding experimental and ANN predicted values of the redox potential at pH=7.0 (E 7 (V) )

Main Results and discu Here are the main results o

In this paper, the Omega and Sadhana polynomials of a new infinite class of Leapfrog fullerenes are computed for the first time. In this paper, we compute the Omega and Sadhana polynomials of the infinite class of fullerenes. Lipid membranes have at least two distinct phases: a tightly ordered phase, often referred to as the "gel phase".

Most of the lipids extracted from such membranes melt in the temperature regime between -200 (some lipids with unsaturations in their chains such as dioleoyl phosphatidylcholine-DOPC) and +60 °C (lipids with a long saturated long chain, e.g. some sphingolipids and ceramides). ). We found that the transition between solid and liquid head group arrangement and the transition between order and disorder of the chains do not necessarily occur at the same temperature and that solid-disordered and liquid-ordered phases are possible. While a solidly disordered phase has so far not been identified in lipid membranes, a fluidly ordered phase is thought to exist in cholesterol-containing membranes, probably due to the size of the cholesterol molecule interfering with the formation of side networks and its hydrogen bonding to the carbonyl oxygen.

The ordered liquid phase is a type of gel phase (i.e., low enthalpy) without lateral packing order. While the transitions mentioned above occur exclusively within the plane of the membrane, there is the possibility of the formation of further lipid phases that utilize curvature changes involving the third dimension normal to the bilayer surface. Lipid membranes exhibit at least two different phases: the solid ordered phase often called the "gel phase" and the fluid-disordered phase often called the "fluid phase".

We have found that the solid-liquid transition of the headgroup order and the order-disorder transition of the chains do not necessarily have to occur at the same temperature and that possibly disordered solid and liquid-ordered phases are possible. The liquid ordered phase is a type of gel phase (ie, low enthalpy) without lateral packing order. In this paper we obtain an accurate shape index of the infinite class of nanostar dendrimers. nnnectivity index, Eccentricity, Nanostar dendrim .. d complex molecules with very well-defined point of view, dendrimers are almost stable sizes and shapes) macromolecules with an onal architecture.

For the comple

Results and discussions Lemma 1. Consider the

The Eccentric Connecti Used Successfully For Predicting Biological Acti Let's be a simple con that is the number of to a vertex that. Main results and discuHere are the main results o Here are the main results o actionable results.2,3. Dendrimers are or generations of a branch of nanotechnology and can be an arithmetic index of two infi Keywords: nanostar dendri 1.

Semnan, Iran. with successive layers key molecules are in the first geometric- .. of edges is tic index 1).

The First Geometric-A We now consider two infin
The Second Geometric Dendrimers

The first geom

Recently, a new topological index (eccentric connectivity index) was defined as ξ(G) = Σu∈V(G)degG(u)ecc(u), where degG(x) denotes the degree of the vertex x in G and ecc( u ) = Max{d(x,u) | x ∈ V(G)}. The eccentricity of a vertex v of G is the maximum distance between v and any other vertex on the graph. In this talk, we present our latest result on eccentric connectivity index for bridge and other related graphs.

In this paper, we apply Klavzar's algorithm to calculate the Wiener index of one pentagonal carbon nanocone. A cactus graph is a connected graph in which no edge lies in more than one cycle. If all blocks of a cactus are G cycles of the same length m, then the cactus is m-uniform.

In this paper, we present a unified approach to the extremal cactus, which has the same or very similar structures, for two types of new indices. In this paper, exact formulas are given for a type of geometric-arithmetic index for Vphenylenic nanotubes. Let G be a connected graph and Sze(G) = We(G) + k, where We(G) and Sze(G) denote the edge-Wiener and edge-Szeged indices of G, respectively.

In this paper, we continue our work to prove that for every connected graph G, Sze(G) = We(G) if and only if G is a tree. The first and second derivatives, in x=1, of Omega polynomial enable the evaluation of the Cluj-Ilmenau CI index.

Index of a combined Coronene-Coronene covering

In this paper we obtain extremal catacondensed hexagonal systems with respect to the GA index. A hexagonal system is a connected geometric figure obtained by arranging regular congruent hexagons in a plane, so that two hexagons are either disjoint or have a common edge. Hexagonal systems are of considerable importance in theoretical chemistry because they are the natural graphical representation of benzenoid hydrocarbons.

A vertex shared by three hexagons is called an internal vertex; the number of internal vertices of a hexagonal system is denoted by ni. Every branched and corner-connected hexagon in a catacondensed hexagonal system is said to be a kink, in Figure 1 the kinks are labeled by K. K K. Initially, we define a concept related to a hexagonal system and use it to describe the GA index of a hexagonal system.

A hexagon in a hexagonal system is called a cubic hexagon if the degree of all vertices is equal to 3. Throughout this paper, we assume that HS is a hexagonal system with n vertices, m edges, h hexagons, hi cubic hexagons, and no interior vertices. A hexagonal system is a connected planar graph with no cut vertices in which all interior faces are hexagons (and all hexagons are faces) such that no two hexagons are disjoint or have exactly one edge in common and no three hexagons share an edge. In this paper, we present a new method for describing hexagonal systems such that a simple graph corresponds to each hexagonal system.

In this article, we present a new method for describing hexagonal systems by associating a simple graph with each hexagonal system. First we define a graph related to a hexagonal system and use it to describe some hexagonal systems. It is easy to see that for any hexagonal system HS, GHS is planner and ∆(GHS)≤6.

Alireza Ashrafi Alir.ashrafi@gmail.com Universiteit van Kashan Jalal Askari Farsangi askari@kashanu.ac.ir Universiteit van Kashan. Tomislav Doslic doslic@master.grad.hr Universiteit van Zagreb, Cratia Hossein Ebrahimpour ebrahimpour@gmail.com Universiteit van Kashan. Azam Giahtazeh a.giahtazeh@modares.ac.ir Tarbiat Modares Universiteit Ante Graovac Ante.Graovac@irb.hr Ruder Boskovic Instituut, Kroasië Roghaye Hafezieh r.hafezieh@yahoo.com Yazd Universiteit.

Hossein Hashemi hossein_hashemi69@yahoo.com SRTT യൂണിവേഴ്സിറ്റി Somayeh Heidari Rad hani5308@yahoo.com SRTT യൂണിവേഴ്സിറ്റി മഹ്സ ഹെമ്മസി mahsa.hemmasi@gmail.com Islamitiese Azad Universiteit. Hosseinzadeh Ma.hoseinzade@gmail.com ശരീഫ് യൂണിവേഴ്‌സിറ്റി സമാനെ ഹൊസൈൻസാദെഹ് hosseinzadeh.samaneh@yahoo.com യൂണിവേഴ്‌സിറ്റി വാൻ കഷൻ സെയ്ദ് മൊഹ്‌സെൻ ജദ്ദി. Leila Jadidoleslam l.jadidolslam@modares.ac.ir Tarbiat Modares Universiteit Nasrin Kahkeshani n.kahkeshan62@gmail.com Qom Universiteit.

Sima Mehdishishvan sima_mehdishishvan@yahoo.com SRTT University Mahsa Mirzargar m.mirzargar@gmail.com University of Kashan. Mojgan Mogharrab mmogharab@gmail.com Persian Gulf University, Bushehr Afshan Mohajeri amohajeri@shirazu.ac.ir Shiraz University. Zohreh Mohammadabadi mohammadabadi.z@gmail.com University of Kashan Abbas Mohammadi abbasmohammadi59@gmail.com Teheran University Marjan Moradi marjanmoradi64@gmail.com Semnan University.

Maryam Rafeipor m.rafeipor@modares.c.ir Tarbiat Modares University Mohamad Rezaee mohamadrezaee@yahoo.com Shahid Beheshti University Mohamad Reza Rostami rostami.mohamadreza@gmail.com Arak University. Hossein Shabani shabani@grad.kashanu.ac.ir University of Kashan Khadijeh Shahsavan Kh.shahsavan@yahoo.com SRTT University. Damir Vukicevic vukicevi@pmfst.hr University of Split, Kroatien Zahra Yarahmadi z.yarahmadi@gmail.com Islamic Azad University of.