scholarly journals Relating Estrada index with spectral radius

2007 ◽  
Vol 72 (12) ◽  
pp. 1321-1327 ◽  
Author(s):  
Ivan Gutman ◽  
Slavko Radenkovic ◽  
Boris Furtula ◽  
Toufik Mansour ◽  
Matthias Schork
Keyword(s):  
Molecular Structure ◽  
Spectral Radius ◽  
Organic Molecules ◽  
Molecular Graph ◽  
3D Structure ◽  
Estrada Index ◽  
Basic Characteristics ◽  
Structure Descriptor ◽  
Long Chain

The Estrada index EE is a recently proposed molecular structure-descriptor, used in the modeling of certain features of the 3D structure of organic molecules, in particular of the degree of folding of proteins and other long-chain biopolymers. The Estrada index is computed from the spectrum of the molecular graph. Therefore, finding its relation with the spectral radius r (= the greatest graph eigenvalue) is of interest, especially because the structure-dependency of r is relatively well understood. In this work, the basic characteristics of the relation between EE and r, which turned out to be much more complicated than initially anticipated, was determined.

Alkanes with Greatest Estrada Index

2007 ◽  
Vol 62 (9) ◽  
pp. 495-498 ◽  
Author(s):  
Ivan Gutman ◽  
Boris Furtula ◽  
Violeta Marković ◽  
Biljana Glišić
Keyword(s):  
Molecular Structure ◽  
Molecular Graph ◽  
Molecular Graphs ◽  
Estrada Index ◽  
Structure Descriptor

If λ1 >λ2 ≥λ3 ≥ · · · ≥λn are the eigenvalues of the molecular graph, then the Estrada index, a recently conceived molecular structure-descriptor is EE = nΣ i=1eλi . The same alkanes, whose molecular graphs have extremal Wiener indices and λ1, are shown to be also extremal with regard to the Estrada index.

scholarly journals Relating the ABC and harmonic indices

2014 ◽  
Vol 79 (5) ◽  
pp. 557-563 ◽  
Author(s):  
Ivan Gutman ◽  
Lingping Zhong ◽  
Kexiang Xu
Keyword(s):  
Molecular Structure ◽  
Topological Index ◽  
Molecular Graph ◽  
Vertex Degree ◽  
Harmonic Index ◽  
Abc Index ◽  
Atom Bond ◽  
Structure Descriptor

The atom-bond connectivity (ABC) index is a much-studied molecular structure descriptor, based on the degrees of the vertices of the molecular graph. Recently, another vertex-degree-based topological index - the harmonic index (H) - attracted attention and gained popularity. We show how ABC and H are related.

Estrada Index of Benzenoid Hydrocarbons

2007 ◽  
Vol 62 (5-6) ◽  
pp. 254-258
Author(s):  
Ivan Gutman ◽  
Slavko Radenković
Keyword(s):  
Molecular Graph ◽  
Benzenoid Hydrocarbons ◽  
Estrada Index ◽  
Carbon Carbon Bonds ◽  
Carbon Bonds ◽  
Structure Descriptor

A structure-descriptor EE, recently proposed by Estrada, is examined. If λ1, λ2, . . . ,λn are the eigenvalues of the molecular graph, then . In the case of benzenoid hydrocarbons with n carbon atoms and m carbon-carbon bonds, EE is found to be accurately approximated by means of the formula a1 n cosh (√2m/n)+a2, where a1 ≈ 1.098 and a2 = −0.64 are empirically determined fitting constants. Within classes of benzenoid isomers (which all have equal n and m), the Estrada index is linearly proportional to the number of bay regions.

Extended energy and its dependence on molecular structure

2017 ◽  
Vol 95 (5) ◽  
pp. 526-529 ◽  
Author(s):  
Ivan Gutman ◽  
Boris Furtula ◽  
Kinkar Ch. Das
Keyword(s):  
Molecular Structure ◽  
Electron Energy ◽  
Topological Index ◽  
Molecular Properties ◽  
Vertex Degree ◽  
Energy Formula ◽  
The Difference ◽  
Basic Characteristics ◽  
Ga Index ◽  
Structure Descriptor

The extended energy ([Formula: see text]) is a vertex degree based and spectrum-based molecular structure descriptor, shown to be well correlated with a variety of physicochemical molecular properties. We investigate the dependence of [Formula: see text] on molecular structure and establish its basic characteristics. In particular, we show how [Formula: see text] is related with the geometric–arithmetic (GA) topological index. Our main finding is that the difference between [Formula: see text] and the total π-electron energy is linearly proportional to the difference between the number of edges and the GA index.

scholarly journals On revised szeged spectrum of a graph

2014 ◽  
Vol 45 (4) ◽  
pp. 375-387 ◽  
Author(s):  
Nader Habibi ◽  
Ali Reza Ashrafi
Keyword(s):  
Molecular Structure ◽  
Adjacency Matrix ◽  
Molecular Graph ◽  
Szeged Index ◽  
Sum Of Products ◽  
Structure Descriptor ◽  
Spectrum Of Graphs

The revised Szeged index is a molecular structure descriptor equal to the sum of products $[n_u(e) + \frac{n_0(e)}{2}][n_v(e) + \frac{n_0(e)}{2}]$ over all edges $e = uv$ of the molecular graph $G$, where $n_0(e)$ is the number of vertices equidistant from $u$ and $v$, $n_u(e)$ is the number of vertices closer to $u$ than $v$ and $n_v(e)$ is defined analogously. The adjacency matrix of a graph weighted in this way is called its revised Szeged matrix and the set of its eigenvalues is the revised Szeged spectrum of $G$. In this paper some new results on the revised Szeged spectrum of graphs are presented.

Eccentric Connectivity Index of Molecular Grapgs of Chemical Trees with Application to Alkynes

2016 ◽  
Vol 13 (10) ◽  
pp. 6694-6697 ◽  
Author(s):  
R. S Haoer ◽  
K. A Atan ◽  
A. M Khalaf ◽  
M. R. Md Said ◽  
R Hasni
Keyword(s):  
Molecular Structure ◽  
Mathematical Modelling ◽  
Biological Activities ◽  
Molecular Graph ◽  
Connectivity Index ◽  
Chemical Bonds ◽  
Eccentric Connectivity Index ◽  
Degree Of A Vertex ◽  
Structure Descriptor ◽  
Chemical Trees

Let G = (V,E) be a simple connected molecular graph. The eccentric connectivity index ξ(G) is a distance–based molecular structure descriptor that was recently used for mathematical modelling of biological activities of diverse nature. In such a simple molecular graph, vertices represent atoms and edges represent chemical bonds, we denoted the sets of vertices and edges by V = V(G) and E = E(G), respectively. If d(u,v) be the notation of distance between vertices u,v ∈ V and is defined as the length of a shortest path connecting them. Then, the eccentricity connectivity index of a molecular graph Gis defined as ξ(G) = Σv∈V(G) deg(V)ec(V), where deg(V) (or simply dv) is degree of a vertex V ∈ V(G), and is defined as the number of adjacent vertices with V. ec(V) is defined as the length of a maximal path connecting to another vertex of v. In this paper, we establish the general formulas for the eccentricity connectivity index of molecular graphs classes of chemical trees with application to alkynes.

Estimating the Laplacian Energy-Like Molecular Structure Descriptor

2012 ◽  
Vol 67 (6-7) ◽  
pp. 403-406 ◽  
Author(s):  
Ivan Gutman
Keyword(s):  
Molecular Structure ◽  
Spanning Trees ◽  
Molecular Graph ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Laplacian Energy ◽  
Number Of Spanning Trees ◽  
Structure Descriptor ◽  
Better Than

Lower and upper bounds for the Laplacian energy-like (LEL) molecular structure descriptor are obtained, better than those previously known. These bonds are in terms of number of vertices and edges of the underlying molecular graph and of graph complexity (number of spanning trees)

scholarly journals On atom-bond connectivity molecule structure descriptors

2016 ◽  
Vol 81 (3) ◽  
pp. 271-276 ◽  
Author(s):  
Boris Furtula ◽  
Ivan Gutman ◽  
Kinkar Das
Keyword(s):  
Molecular Structure ◽  
Connectivity Index ◽  
Benzenoid Hydrocarbons ◽  
Molecule Structure ◽  
New Variant ◽  
Basic Characteristics ◽  
Atom Bond ◽  
Structure Descriptor

The atom-bond connectivity index (ABC) is a degree-based molecular structure descriptor with well-documented chemical applications. In 2010 a distance-based new variant of this index (ABCGG) has been proposed. Until now, the relation between ABC and ABCGG has not been analyzed. In this paper, we establish the basic characteristics of this relation. In particular, ABC and ABCGG are not correlated and both cases ABC > ABCGG and ABC < ABCGG may occur in the case of (structurally similar) molecules. However, in the case of benzenoid hydrocarbons, ABC always exceeds ABCGG.

MUFFIN: multi-scale feature fusion for drug–drug interaction prediction

2021 ◽  
Author(s):  
Yujie Chen ◽  
Tengfei Ma ◽  
Xixi Yang ◽  
Jianmin Wang ◽  
Bosheng Song ◽  
...  
Keyword(s):  
Molecular Structure ◽  
Deep Learning ◽  
Medical Information ◽  
Feature Fusion ◽  
Molecular Graph ◽  
Knowledge Graph ◽  
Sequence Information ◽  
Learning Models ◽  
Scale Feature ◽  
Multi Scale

Abstract Motivation Adverse drug–drug interactions (DDIs) are crucial for drug research and mainly cause morbidity and mortality. Thus, the identification of potential DDIs is essential for doctors, patients and the society. Existing traditional machine learning models rely heavily on handcraft features and lack generalization. Recently, the deep learning approaches that can automatically learn drug features from the molecular graph or drug-related network have improved the ability of computational models to predict unknown DDIs. However, previous works utilized large labeled data and merely considered the structure or sequence information of drugs without considering the relations or topological information between drug and other biomedical objects (e.g. gene, disease and pathway), or considered knowledge graph (KG) without considering the information from the drug molecular structure. Results Accordingly, to effectively explore the joint effect of drug molecular structure and semantic information of drugs in knowledge graph for DDI prediction, we propose a multi-scale feature fusion deep learning model named MUFFIN. MUFFIN can jointly learn the drug representation based on both the drug-self structure information and the KG with rich bio-medical information. In MUFFIN, we designed a bi-level cross strategy that includes cross- and scalar-level components to fuse multi-modal features well. MUFFIN can alleviate the restriction of limited labeled data on deep learning models by crossing the features learned from large-scale KG and drug molecular graph. We evaluated our approach on three datasets and three different tasks including binary-class, multi-class and multi-label DDI prediction tasks. The results showed that MUFFIN outperformed other state-of-the-art baselines. Availability and implementation The source code and data are available at https://github.com/xzenglab/MUFFIN.

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