scholarly journals Comparison between the Wiener index and the Zagreb indices and the eccentric connectivity index for trees

2014 ◽  
Vol 171 ◽  
pp. 35-41 ◽  
Author(s):  
Kinkar Ch. Das ◽  
Han-ul Jeon ◽  
Nenad Trinajstić
Keyword(s):  
Wiener Index ◽  
Connectivity Index ◽  
Eccentric Connectivity Index ◽  
Zagreb Indices

On the eccentric connectivity index and Wiener index of a graph

2014 ◽  
Vol 37 (1) ◽  
pp. 39-47 ◽  
Author(s):  
P. Dankelmann ◽  
M.J. Morgan ◽  
S. Mukwembi ◽  
H.C. Swart
Keyword(s):  
Wiener Index ◽  
Connectivity Index ◽  
Eccentric Connectivity Index

scholarly journals Network Similarity Measure and Ediz Eccentric Connectivity Index

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Guihai Yu ◽  
Xinzhuang Chen
Keyword(s):  
Similarity Measure ◽  
Similarity Measures ◽  
Wiener Index ◽  
Topological Indices ◽  
Connectivity Index ◽  
Laplacian Eigenvalue ◽  
Eccentric Connectivity Index ◽  
Graph Energy ◽  
Network Similarity ◽  
The One

Network similarity measures have proven essential in the field of network analysis. Also, topological indices have been used to quantify the topology of networks and have been well studied. In this paper, we employ a new topological index which we call the Ediz eccentric connectivity index. We use this quantity to define network similarity measures as well. First, we determine the extremal value of the Ediz eccentric connectivity index on some network classes. Second, we compare the network similarity measure based on the Ediz eccentric connectivity index with other well-known topological indices such as Wiener index, graph energy, Randić index, the largest eigenvalue, the largest Laplacian eigenvalue, and connectivity eccentric index. Numerical results underpin the usefulness of the chosen measures. They show that our new measure outperforms all others, except the one based on Wiener index. This means that the measure based on Wiener index is still the best, but the new one has certain advantage to some extent.

Further results on Zagreb eccentricity coindices

2020 ◽  
Vol 12 (06) ◽  
pp. 2050075
Author(s):  
Mahdieh Azari
Keyword(s):  
Wiener Index ◽  
Connectivity Index ◽  
Lower And Upper Bounds ◽  
Graph Invariants ◽  
Eccentric Connectivity Index ◽  
Size Number ◽  
Connectivity Indices ◽  
Degree Distance ◽  
Graph Parameters ◽  
Eccentric Distance

The eccentric connectivity index and second Zagreb eccentricity index are well-known graph invariants defined as the sums of contributions dependent on the eccentricities of adjacent vertices over all edges of a connected graph. The coindices of these invariants have recently been proposed by considering analogous contributions from the pairs of non-adjacent vertices. Here, we obtain several lower and upper bounds on the eccentric connectivity coindex and second Zagreb eccentricity coindex in terms of some graph parameters such as order, size, number of non-adjacent vertex pairs, radius, and diameter, and relate these invariants to some well-known graph invariants such as Zagreb indices and coindices, status connectivity indices and coindices, ordinary and multiplicative Zagreb eccentricity indices, Wiener index, degree distance, total eccentricity, eccentric connectivity index, second eccentric connectivity index, and eccentric-distance sum. Moreover, we compute the values of these coindices for two graph constructions, namely, double graphs and extended double graphs.

TOPOLOGICAL MODELS FOR THE PREDICTION OF NEUTRAL ENDOPEPTIDASE AND ANGIOTENSIN-CONVERTING ENZYME INHIBITORY ACTIVITY OF MERCAPTOACYLDIPEPTIDES

2006 ◽  
Vol 05 (03) ◽  
pp. 565-577 ◽  
Author(s):  
VINEY LATHER ◽  
A. K. MADAN
Keyword(s):  
Inhibitory Activity ◽  
Topological Index ◽  
Wiener Index ◽  
Neutral Endopeptidase ◽  
Connectivity Index ◽  
Molecular Connectivity ◽  
Ace Inhibitory Activity ◽  
Eccentric Connectivity Index ◽  
Data Set ◽  
Molecular Connectivity Index

The relationship between the topological indices and the Neutral Endopeptidase (NEP) inhibitory activity and Angiotensin-Converting Enzyme (ACE) inhibitory activity of mercaptoacyldipeptides has been investigated. Three topological indices — the Wiener index (a distance-based topological index), the molecular connectivity index (an adjacency-based topological index), and the eccentric connectivity index (an adjacency-cum-distance-based topological index), were presently used for investigation. A data set comprising 39 differently substituted mercaptoacyldipeptides was selected for the present study. The values of the Wiener index, molecular connectivity index, and eccentric connectivity index for each of the 39 compounds comprising the data set were computed using an in-house computer program. Resultant data were analyzed and suitable models were developed after identification of the active ranges. Subsequently, a biological activity was assigned to each compound using these models, and the biological activity was then compared with the reported NEP and ACE inhibitory activity of each compound. Accuracy of prediction up to a maximum of ~91% was obtained using these models.

scholarly journals Eccentricity based topological indices of face centered cubic lattice FCC(n)

2020 ◽  
Vol 44 (1) ◽  
pp. 32-38
Author(s):  
Hani Shaker ◽  
Muhammad Imran ◽  
Wasim Sajjad
Keyword(s):  
Wiener Index ◽  
Face Centered Cubic ◽  
Eccentric Connectivity Index ◽  
Zagreb Index ◽  
Cubic Lattice ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Wide Range ◽  
Unit Cells ◽  
Face Centered

Abstract Chemical graph theory has become a prime gadget for mathematical chemistry due to its wide range of graph theoretical applications for solving molecular problems. A numerical quantity is named as topological index which explains the topological characteristics of a chemical graph. Recently face centered cubic lattice FCC(n) attracted large attention due to its prominent and distinguished properties. Mujahed and Nagy (2016, 2018) calculated the precise expression for Wiener index and hyper-Wiener index on rows of unit cells of FCC(n). In this paper, we present the ECI (eccentric-connectivity index), TCI (total-eccentricity index), CEI (connective eccentric index), and first eccentric Zagreb index of face centered cubic lattice.

On eccentricity-based topological descriptors of water-soluble dendrimers

2018 ◽  
Vol 74 (1-2) ◽  
pp. 25-33 ◽  
Author(s):  
Zahid Iqbal ◽  
Muhammad Ishaq ◽  
Adnan Aslam ◽  
Wei Gao
Keyword(s):  
Molecular Structure ◽  
Chemical Properties ◽  
Topological Indices ◽  
Water Soluble ◽  
Connectivity Index ◽  
Topological Descriptors ◽  
Physical And Chemical Properties ◽  
Eccentric Connectivity Index ◽  
Physical And Chemical ◽  
And Chemical Properties

AbstractPrevious studies show that certain physical and chemical properties of chemical compounds are closely related with their molecular structure. As a theoretical basis, it provides a new way of thinking by analyzing the molecular structure of the compounds to understand their physical and chemical properties. The molecular topological indices are numerical invariants of a molecular graph and are useful to predict their bioactivity. Among these topological indices, the eccentric-connectivity index has a prominent place, because of its high degree of predictability of pharmaceutical properties. In this article, we compute the closed formulae of eccentric-connectivity–based indices and its corresponding polynomial for water-soluble perylenediimides-cored polyglycerol dendrimers. Furthermore, the edge version of eccentric-connectivity index for a new class of dendrimers is determined. The conclusions we obtained in this article illustrate the promising application prospects in the field of bioinformatics and nanomaterial engineering.

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